The On-Line Encyclopedia of Integer Sequences, Recent Additions

This is a section of the main database for the On-Line Encyclopedia of Integer Sequences.

It shows the most recently added sequences in reverse chronological order.

For more information see the following pages:
( www.research.att.com/~njas/sequences/ then )

    Seis.html:          Welcome
    index.html:         Lookup 
    demo1.html:         Demos 
    Sindx.html:         Index 
    WebCam.html:        WebCam
    Submit.html:        Contribute new sequence or comment 
    eishelp1.html:      Internal format 
    eishelp2.html:      Beautified format
    transforms.html:    Transforms 
    Spuzzle.html:       Puzzles 
    Shot.html:          Hot 
    classic.html:       Classics
    ol.html:            Superseeker 
    pages.html:         More pages 

Maintained  by:         N. J. A. Sloane (njas@research.att.com), 
    home page:          www.research.att.com/~njas/
    

The WebCam at www.research.att.com/~njas/sequences/WebCam.html
is another way to browse the recent additions.

[If the database has just been resorted into lexicographic order,
the present file will be empty, but the WebCam will still work.]

(start)

%I A167423
%S A167423 1,1,11,50,186,631,2029,6299,19075,56704,166164,481391,
%T A167423 1381691,3935125,11134331,31328366,87721614,244588519,679429225,
%U A167423 1881102959,5192705779,14296088956,39263958696,107601905375
%V A167423 1,-1,-11,-50,-186,-631,-2029,-6299,-19075,-56704,-166164,-481391,
%W A167423 -1381691,-3935125,-11134331,-31328366,-87721614,-244588519,-679429225,
%X A167423 -1881102959,-5192705779,-14296088956,-39263958696,-107601905375
%N A167423 Hankel transform of a simple Catalan convolution.
%C A167423 Hankel transform of A167422.
%F A167423 G.f.: (1-7x+6x^2-x^3)/(1-6x+11x^2-6x^3+x^4).
%K A167423 easy,sign,new
%O A167423 0,3
%A A167423 Paul Barry (pbarry(AT)wit.ie), Nov 03 2009

%I A167422
%S A167422 1,2,3,7,19,56,174,561,1859,6292,21658,75582,266798,950912,3417340,
%T A167422 12369285,45052515,165002460,607283490,2244901890,8331383610,
%U A167422 31030387440,115948830660,434542177290,1632963760974,6151850548776
%N A167422 Expansion of (1+x)*c(x), c(x) the g.f. of A000108.
%C A167422 Hankel transform is A167423.
%F A167422 a(n)=sum{k=0..n, A000108(k)*C(1,n-k)}.
%K A167422 easy,nonn,new
%O A167422 0,2
%A A167422 Paul Barry (pbarry(AT)wit.ie), Nov 03 2009

%I A167421
%S A167421 1,2,4,8,16,10,20,18,14,6,12,2,4,8,16,10,20,18,14,6,12,2,4,8,16,10,20,
%T A167421 18,14,6,12,2,4,8,16,10,20,18,14,6,12,2,4,8,16,10,20,18,14,6,12,2,4,8,
%U A167421 16,10,20,18,14,6,12,2,4,8,16,10,20,18,14,6,12,2,4,8,16,10,20,18,14,6
%N A167421 2^n mod 22.
%o A167421 (Other) sage: [power_mod(2,n,22)for n in xrange(0,84)] #
%K A167421 nonn,new
%O A167421 0,2
%A A167421 Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 03 2009

%I A167420
%S A167420 1,2,4,8,2,4,8,2,4,8,2,4,8,2,4,8,2,4,8,2,4,8,2,4,8,2,4,8,2,4,8,2,4,8,2,
%T A167420 4,8,2,4,8,2,4,8,2,4,8,2,4,8,2,4,8,2,4,8,2,4,8,2,4,8,2,4,8,2,4,8,2,4,8,
%U A167420 2,4,8,2,4,8,2,4,8,2,4,8,2,4,8,2,4,8,2,4,8,2,4,8,2,4,8,2,4,8
%N A167420 2^n mod 14.
%o A167420 (Other) sage: [power_mod(2,n,14)for n in xrange(0,100)] #
%K A167420 nonn,new
%O A167420 0,2
%A A167420 Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 03 2009

%I A167419
%S A167419 2,1,4,3,6,5,8,7,9,11,10,13,12,14,15,17,16,19,18,20,21,23,22,24,25,26,
%T A167419 27,29,28,31,30,32,33,34,35,37,36,38,39,41,40,44,43,45,47,46,48,49,50,
%U A167419 51,53,52,54,55,56,57,59,58,61,60,62,63,65,65,67,66,68,69,71,70,73,72
%N A167419 Exchange no-primes and primes.
%Y A167419 Cf. A014681
%K A167419 easy,nonn,new
%O A167419 1,1
%A A167419 Giovanni Teofilatto (g.teofilatto(AT)tiscalinet.it), Nov 03 2009

%I A167418
%S A167418 1,4,11,124,841,3844,23571,159164,903201,5174084,32096731,192836604,
%T A167418 1128271161,6758574724,40676603491,241740656444,1439437080721,
%U A167418 8616705389764,51443701799851,306634988322684,1830991983267881
%N A167418 A toral inverse expansion of the polynomial times 5^(n+1): p(x)=5*x^3 - 4*x^2 + x - 4
%C A167418 Three comments:
%C A167418 1) the polynomial has a root near the second smallest Salem number1.1883681475082235... at:
%C A167418 1.1938049139642297...
%C A167418 2) the signature sequences of the two constants to the 95th term are the same:
%C A167418 A167289.
%C A167418 3) the limiting ratio of the terms
%C A167418 a[n+1]/a[n] approaches 5*1.1938049139642297....
%t A167418 Clear[p.q, x, t, n]
%t A167418 p[x_] = 5*x^3 - 4*x^2 + x - 4
%t A167418 q[x_] = 1/Expand[x^3*p[1/x]]
%t A167418 Table[5^(n + 1)*SeriesCoefficient[ Series[q[t], {t, 0, 60}], n], {n, 0, 60}]
%Y A167418 A167289
%K A167418 nonn,uned,new
%O A167418 0,2
%A A167418 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 03 2009

%I A167417
%S A167417 2,23,523,7523,751123,71151323,7115117323,711913152317,71231915117323
%N A167417 a(n) is n-th prime (n > 1, a(1)=2) put to a prime concatenation of first n-1 primes (not necessary to a(n-1)) so that the result is largest possible PRIME
%C A167417 Sequence is finite (9 terms only), because sum of first 10 primes: 2+3+5+7+11+13+17+19+23+29 = 3 * 43
%D A167417 A. Weil, Number theory: an approach through history, Birkhaeuser 1984
%D A167417 Richard E. Crandall, Carl Pomerance, Prime Numbers, Springer 2005
%D A167417 Paulo Ribenboim, The New Book of Prime Number Records, Springer 1996
%e A167417 (1) for a(1)=2, a(2)=23, a(3)=523 no other possibility
%e A167417 (2) for calculating a(4) the 4th prime 7 is to concatenate: 5237, 5273, 7523 are prime (but 5723=59 * 97) => largest is a(4) = 7523
%e A167417 (3) a(6) is not formed of 6th prime 13 and a(5)=751123 but from 711523 and 13
%K A167417 fini,nonn,new
%O A167417 1,1
%A A167417 Dr. Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 03 2009

%I A167416
%S A167416 2,23,523,5237,115237,11315237,1117523137,111752313719,11175231371923
%N A167416 a(n) is n-th prime (n > 1, a(1)=2) put to a prime concatenation of first n-1 primes (not necessary to a(n-1)) so that the result is smallest possible PRIME
%C A167416 Sequence is finite (9 terms only), because sum of first 10 primes: 2+3+5+7+11+13+17+19+23+29 = 3 * 43
%D A167416 A. Weil, Number theory: an approach through history, Birkhaeuser 1984
%D A167416 Richard E. Crandall, Carl Pomerance, Prime Numbers, Springer 2005
%D A167416 Paulo Ribenboim, The New Book of Prime Number Records, Springer 1996
%e A167416 (1) for a(1)=2, a(2)=23, a(3)=523 no other possibility
%e A167416 (2) for calculating a(4) the 4th prime 7 is to concatenate: 5237, 5273, 7523 are prime (but 5723=59 * 97) => smallest is a(4) = 5237
%e A167416 (3) a(7) is not formed of 7th prime 17 and a(6)=11315237 but from 11523137 and 17
%K A167416 fini,nonn,new
%O A167416 1,1
%A A167416 Dr. Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 03 2009

%I A167415
%S A167415 2,3,6,7,13,14,17,21,23,26,34,37,39,42,43,46,47,51,53,67,69,73,74,78,83,
%T A167415 86,91,94,97,102
%N A167415 Positives integers n such as there is no solution of the equation xA^2 +yA^2 +3*x*y = 0 in Z/nZ except for the trivial one (0,0)
%C A167415 Prime numbers of this sequence are congruent to {2,3} modulo 5
%e A167415 The only solution of the equation xA^2 +yA^2 +3*x*y = 0 in Z/2Z is (0,0)
%K A167415 easy,nonn,new
%O A167415 1,1
%A A167415 Arnaud Vernier (arnaud.vernier(AT)ecl2008.ec-lyon.fr), Nov 03 2009

%I A167414
%S A167414 127,149,211,251,271,277,347,419,457,491,521,523,541,547,587,727,743,
%T A167414 853,857,941
%N A167414 Primes p such that sum of digits^2-1 is prime
%C A167414 127 to this sequence because 1^2+2^2+7^2-1=53 (prime); 149 because 1^2+4^2+9^2-1=97; 347 because 3^2+4^2+7^2-1=73
%K A167414 nonn,new
%O A167414 1,1
%A A167414 Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 03 2009

%I A167413
%S A167413 2,2,1,3,1,3,1,3,1,3,1,1,4,1,1,4,1,1,4,1,1,4,1,1,4,1,1,4,1,1,1,5,1,1,1,
%T A167413 5,1,1,1,5,1,1,1,5,1,1,1,5,1,1,1,5,1,1,1,5,1,1,1,5,1,1,1,1,6,1,1,1,1,6,
%U A167413 1,1,1,1,6,1,1,1,1,6,1,1,1,1,6,1,1,1,1,6,1,1,1,1,6,1,1,1,1,6,1,1,1,1,6
%N A167413 First differences of A167384=1,3,5,6,9,10,13,14,17,.
%C A167413 From a mathematical array for periodic table of the elements (linked to Janet form). There are respectively 2n+2=A005843 2's,3's,4's,5's,6's=A000027(n+1). a(n) is a double sequence ie double b(n)=2,1,3,1,3,1,1,4,1,1,4,1,1,4,1,1,1,5,1,1,1,5,1,1,1,5,1,1,1,5,1,1,1,1,6,. Note a(n) taken by (2,2,4,4,4,4,6,6,6,6,6,6,8,=A001670)/2=1,1,2,2,2,2,3,3,3,3,3,3,4,=A000194 terms have sum 2,2,4,4,4,4,6,6,6,6,6,6,8,8,8,8,8,8,8,8,10,=A001670. See A167381=1,3,6,10,14,18,23,29,.
%K A167413 nonn,uned,new
%O A167413 0,1
%A A167413 Paul Curtz (bpcrtz(AT)free.fr), Nov 03 2009

%I A167412
%S A167412 11,13,19,31,37,59,73,79,97,101,103,109,163,181,251,257,277,307,349,383,
%T A167412 439,499,509,521,541,563,587,613,631,653
%N A167412 Primes p such that sum of digits^2+1 is prime.
%C A167412 11 to this sequence because 1^2+1^2+1=3 (prime); 163 because 1^2+6^2+3^2+1=47; 277 because 2^2+7^2+7^2+1=103
%K A167412 nonn,new
%O A167412 1,1
%A A167412 Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 03 2009

%I A167411
%S A167411 2,3,3,5,5,7,3,7,11,3,17,7,3,5,3,29,5,5,3,41,3,7,3,5,5,3,59,5,7,3,13,71,
%T A167411 7,7,3,5,3,5,3,101,3,107,3,7,5,7,5,3,5,3,137,3,149,5,5,11,7,7,3,3,5,5,3,
%U A167411 179,7,3,191,3,197,5,11,5,13,3,227,3,7,5,3,239,7,7,5,3,11,3,3,5,3
%N A167411 a(n) = the minimal K value for the orderly number A167408(n).
%e A167411 a(6) = 7, because A167408(6) = 9, and divisors of 9 = {1,9,3} == {1,2,3} mod 7.
%Y A167411 Cf. A167408 - Orderly Numbers
%Y A167411 Cf. A167409 - Very Orderly Numbers ( K = tau(N)+1 )
%Y A167411 Cf. A167410 - Disorderly Numbers - numbers not in A167408
%K A167411 nonn,new
%O A167411 1,1
%A A167411 Andrew Weimholt (andrew(AT)weimholt.com), Nov 03 2009

%I A167410
%S A167410 3,4,6,10,14,15,16,18,21,22,24,25,26,28,30,32,33,34,35,36,39,40,42,44,
%T A167410 45,46,48,49,50,51,54,55,56,60,62,63,64,65,66,69,70,74,75,77,78,80,81,
%U A167410 82,84,85,86,88,90,91,92,93,94,95,96,98,99,100,102,104,105,106,108
%N A167410 Disorderly Numbers: numbers not in A167408 (orderly numbers).
%e A167410 3 is disorderly because there exists no K > 2=tau(3), such that {1,3} == {1,2} mod K.
%Y A167410 Cf. A167408 - Orderly Numbers
%Y A167410 Cf. A167409 - Very Orderly Numbers ( K = tau(N)+1 )
%Y A167410 Cf. A167411 - Minimal K Values for the Orderly Numbers
%K A167410 nonn,new
%O A167410 1,1
%A A167410 Andrew Weimholt (andrew(AT)weimholt.com), Nov 03 2009

%I A167409
%S A167409 1,2,5,8,11,12,17,20,23,27,29,38,41,47,52,53,57,58,59,68,71,72,76,83,87,
%T A167409 89,101,107,113,117,118,124,131,133,137,149,158,162,164,167,173,177,178,
%U A167409 179,188,191,197,203,218,227,233,236,237,239,243,244,247,251,257
%N A167409 Very Orderly Numbers: a number, N, is "very orderly" if the set of the divisors of N is congruent to the set {1,2,...,tau(N)} mod tau(N)+1.
%C A167409 The very orderly numbers are orderly numbers (Cf. A167408) with K = tau(N)+1
%o A167409 (PARI)
%o A167409 vo(n)=#(n=divisors(n))==#(n=Set(n%(1+#n))) & n[1]!="0"
%o A167409 for(n=1,999,vo(n)&print1(n", "))
%o A167409 --Maximilian Hasler
%Y A167409 Cf. A167408 - Orderly Numbers
%Y A167409 Cf. A167410 - Disorderly Numbers - numbers not in A167408
%Y A167409 Cf. A167411 - Minimal K Values for the Orderly Numbers
%K A167409 nonn,new
%O A167409 1,2
%A A167409 Andrew Weimholt (andrew(AT)weimholt.com), Nov 03 2009

%I A167408
%S A167408 1,2,5,7,8,9,11,12,13,17,19,20,23,27,29,31,37,38,41,43,47,52,53,57,58,
%T A167408 59,61,67,68,71,72,73,76,79,83,87,89,97,101,103,107,109,113,117,118,124,
%U A167408 127,131,133,137,139,149,151,157,158,162,163,164,167,173,177,178,179
%N A167408 Orderly Numbers: a number, N, is orderly if there exists some number K > tau(N), such that the set of the divisors of N is congruent to the set {1,2,...,tau(N)} mod K.
%C A167408 . N: {divisors(N)} == {1,2,...,tau(N)} mod K
%C A167408 . -------------------------------------------
%C A167408 . 1: {1} == {1} mod 2
%C A167408 . 2: {1,2} == {1,2} mod 3
%C A167408 . 5: A {1,5} == {1,2} mod 3
%C A167408 . 7: A {1,7} == {1,2} mod 5
%C A167408 . 8: A {1,2,8,4} == {1,2,3,4} mod 5
%C A167408 . 9: A {1,9,3} == {1,2,3} mod 7
%C A167408 . 11: A {1,11} == {1,2} mod 3 or 9
%C A167408 . 12: A {1,2,3,4,12,6} == {1,2,3,4,5,6} mod 7
%C A167408 . 13: A {1,13} == {1,2} mod 11
%C A167408 . 17: A {1,17} == {1,2} mod 3,5, or 15
%C A167408 . 19: A {1,19} == 1,2 mod 17
%C A167408 . 20: A {1,2,10,4,5,20} == {1,2,3,4,5,6} mod 7
%C A167408 . 23: A {1,23} == {1,2} mod 3,7, or 21
%C A167408 . 27: A {1,27,3,9} == {1,2,3,4} mod 5
%C A167408 . 29: A {1,29} == {1,2} mod 3,9, or 27
%C A167408 . 31: A {1,31} == {1,2} mod 29
%C A167408 . 37: A {1,37} == 1,2 mod 5,7, or 35
%C A167408 . 38: A {1,2,38,19} == {1,2,3,4} mod 5
%C A167408 . 41: A {1,41} == {1,2} mod 3,13, or 39
%C A167408 . 43: A {1,43} == {1,2} mod 41
%C A167408 . 47: A {1,47} == {1,2} mod 3,5,9,15, or 45
%C A167408 . 52: A {1,2,52,4,26,13} == {1,2,3,4,5,6} mod 7
%C A167408 . 53: A {1,53} == {1,2} mod 3,17, or 51
%C A167408 . 57: A {1,57,3,19} == {1,2,3,4} mod 5
%C A167408 . 58: A {1,2,58,29} == {1,2,3,4} mod 5
%C A167408 . 59: A {1,59} == {1,2} mod 3,19, or 57
%C A167408 . 61: A {1,61} == {1,2} mod 59
%C A167408 . 67: A {1,67} == {1,2} mod 5,13, or 65
%C A167408 . 68: A {1,2,17,4,68,34} == {1,2,3,4,5,6} mod 7
%C A167408 . 71: A {1,71} == {1,2} mod 3,23, or 69
%C A167408 . 72: A {1,2,3,4,18,6,72,8,9,36,24,12} == {1,2,3,4,5,6,7,8,9,10,11,12} mod 13
%C A167408 . 73: A {1,73} == {1,2} mod 71
%C A167408 . 76: A {1,2,38,4,19,76} == {1,2,3,4,5,6} mod 7
%C A167408 . 79: A {1,79} == {1,2} mod 7,11, or 77
%C A167408 . 83: A {1,83} == {1,2} mod 3,9,27, or 81
%C A167408 . 87: A {1,87,3,29} == {1,2,3,4} mod 5
%C A167408 . 89: A {1,89} == {1,2} mod 3,29, or 87
%C A167408 . 97: A {1,97} == {1,2} mod 5,19, or 95
%C A167408 The primes, except for 3, are orderly.
%C A167408 Numbers of the form 4p are orderly when p is an odd prime congruent to 3,5, or 6 mod 7.
%C A167408 For primes, K values can be p-2, or a divisor of p-2 other than 1.
%C A167408 T. D. Noe observed that for composite orderly numbers, N,
%C A167408 K seems to be one of the three values: tau(n)+1, tau(n)+3, tau(n)+4.
%C A167408 The composite numbers with K = tau(N)+4 are of the form
%C A167408 . p^2, where prime p == 3 mod 7.
%C A167408 The composite orderly numbers with K = tau(N)+3, come in the following forms for K <= 67
%C A167408 . p*q*r with primes {p,q,r} == {3,5,6} mod 11
%C A167408 . p^3*q with primes {p,q} == {5,6} mod 11
%C A167408 . p^3*q with primes {p,q} == {6,5} mod 11
%C A167408 . p^4*q with primes {p,q} == {7,6} mod 13
%C A167408 . p*q*r*s with primes {p,q,r,s} == {5,6,9,10} mod 19
%C A167408 . p^3*q*r with primes {p,q,r} == {5,9,10} mod 19
%C A167408 . p^3*q*r with primes {p,q,r} == {9,6,10} mod 19
%C A167408 . p^3*q*r with primes {p,q,r} == {10,6,9} mod 19
%C A167408 . p*q*r*s*t*u with primes {p,q,r,s,t,u} == {17,21,33,34,39,47} mod 67
%C A167408 . p*q*r*s*t*u with primes {p,q,r,s,t,u} == {19,34,35,36,49,56} mod 67
%C A167408 Note that 11, 19, and 67, are primes of the form 2^x+3.
%C A167408 The forms for composite orderly numbers with K = tau(N)+1 are too numerous to list here, but seem to occur for any prime K > 3.
%e A167408 12 is an orderly number because 12's divisors are 1,2,3,4,5,6 and
%e A167408 . 1 == 1 mod 7
%e A167408 . 2 == 2 mod 7
%e A167408 . 3 == 3 mod 7
%e A167408 . 4 == 4 mod 7
%e A167408 .12 == 5 mod 7
%e A167408 . 6 == 6 mod 7
%Y A167408 Cf. A167409 - Very Orderly Numbers ( K = tau(N)+1 )
%Y A167408 Cf. A167410 - Disorderly Numbers - numbers not in this sequence
%Y A167408 Cf. A167411 - Minimal K Values for the Orderly Numbers
%K A167408 nonn,new
%O A167408 1,2
%A A167408 Andrew Weimholt (andrew(AT)weimholt.com), Nov 03 2009

%I A167154
%S A167154 9,30,49,70,89,200,399,600,799,1000
%N A167154 Numbers where terms in A167153 change parity: a(n)+1 is in A167153, but a(n)-1 is not.
%C A167154 Sequence A167153 consists of runs of numbers of the same parity. It is conjectured that each time the parity changes, there is a gap of 3 numbers, and the sequence goes on with the successor a(n)+1 (of opposite parity) of the first "missing" term a(n) in the run of terms of given parity (a(n-1)+1, a(n-1)+3, ..., a(n)-2).
%H A167154 E. Angelini, <a href="http://www.cetteadressecomportecinquantesignes.com/Digitsum.htm">a(n) is the digitsum of a(a(n))</a>, November 2009.
%e A167154 Sequence A167153 starts 10,12,14,... so a(1)=9 is the predecessor of the first even term 10 = a(1)+1 in the sequence.
%e A167154 Then the sequence changes parity at ...,26, 28, 31, 33,..., i.e. a(2)-2 = 28 is the last term in this run of even numbers, a(2) = 30 is missing, and the sequence goes on with odd numbers starting at a(2)+1 = 31.
%e A167154 That run of odd numbers ends with a(3)-2 = 47; a(3) = 49 is missing, and the sequence goes on with even numbers starting at a(3)+1 = 50.
%Y A167154 Cf. A167152.
%K A167154 more,nice,nonn,new
%O A167154 1,1
%A A167154 Eric Angelini (Eric.Angelini(AT)kntv.be) and M. F. Hasler (MHasler(AT)univ-ag.fr), Nov 03 2009

%I A167155
%S A167155 1,6,1,1,1,1,1,6,2,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%T A167155 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%U A167155 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
%N A167155 Exponential primorial constant sum( 1/A140319(k), k>=0 )
%C A167155 This is a Liouville number and therefore transcendental.
%H A167155 J. Sondow, <a href="http://mathworld.wolfram.com/ExponentialFactorial.html">"Exponential Factorial."</a>
%e A167155 1 + 1/2^1 + 1/3^2 + 1/5^9 + 1/7^(5^9)+ ... = 1.6111116231111111111111111111111111111111...
%e A167155 Since 1/9 = 0.11111... and 1/5^9 = 512*10^(-9), the initial 10 digits are 1.611111623.
%e A167155 Since 1/A140319(4) = 1/7^1953125 = 7.7731519...*10^(-1650583), these digits are followed by a string of 1650573 "1"s, then followed by digits 8884263011....
%o A167155 (PARI) 1+1/2+1/3^2+1/5^9+1/7^5^9. /* The final dot is part of the code! */
%Y A167155 Cf. A080219.
%K A167155 cons,easy,nice,nonn,new
%O A167155 1,2
%A A167155 M. F. Hasler (MHasler(AT)univ-ag.fr), Nov 03 2009

%I A167407
%S A167407 0,1,1,2,1,1,3,1,1,1,4,1,1,1,1,5,1,1,1,1,1,6,1,1,1,1,1,1,7,1,1,1,
%T A167407 1,1,1,1,8,1,1,1,1,1,1,1,1,9,1,1,1,1,1,1,1,1,1,10,1,1,1,1,1,1,1,1,1,
%U A167407 1,11,1,1,1,1,1,1,1,1,1,1,1,12,1,1,1,1,1,1,1,1,1,1,1,1,13,1,1,1,1,1
%V A167407 0,-1,1,-2,1,1,-3,1,1,1,-4,1,1,1,1,-5,1,1,1,1,1,-6,1,1,1,1,1,1,-7,1,1,1,
%W A167407 1,1,1,1,-8,1,1,1,1,1,1,1,1,-9,1,1,1,1,1,1,1,1,1,-10,1,1,1,1,1,1,1,1,1,
%X A167407 1,-11,1,1,1,1,1,1,1,1,1,1,1,-12,1,1,1,1,1,1,1,1,1,1,1,1,-13,1,1,1,1,1
%N A167407 T(m,n) is -m if n=0, 1 elsewhere.
%C A167407 This triangle encodes a family of conditionally convergent series for the logarithm of integers, according to:
%C A167407 log(1+m)=Sum_{n>0} T(m,n mod m)/n
%C A167407 The second row of the triangle, m=1, corresponds to Mercator's series
%C A167407 log(2)=1-1/2+1/3-1/4+1/5-1/6+-...
%C A167407 Triangle begins:
%C A167407 0;
%C A167407 -1,1;
%C A167407 -2,1,1;
%C A167407 -3,1,1,1;
%C A167407 -4,1,1,1,1;
%C A167407 .
%C A167407 .
%C A167407 .
%Y A167407 Cf. A061347, A166711, A166871.
%K A167407 sign,tabf,new
%O A167407 0,4
%A A167407 Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Nov 03 2009

%I A167406
%S A167406 0,4,64,2880,208896,23193600,3640688640,768126320640,209688566169600,
%T A167406 71921062285148160
%N A167406 Sequence a(n) counts the number of ways to seat $2n$ people around a circular table so that person $i$ does not sit across from person $n+i$ for any $1 \leq i \leq n$.
%e A167406 When n=2, there are four people seated around a circular table. Person 1 can sit across from either person 2 or person 4, and person 3 can sit either to the left or to the right of person 1. Thus a(2) = 2*2=4.
%o A167406 (Other) (factorial(n)^2/(2*n))*sum((-1)^k/(factorial(k))*binomial(2*n-2*k,n-k)*2^k for k in range(0,n+1))
%K A167406 nonn,new
%O A167406 1,2
%A A167406 Steven Klee (klees(AT)math.washington.edu), Nov 03 2009

%I A083209
%S A083209 6,12,20,28,56,70,88,104,176,208,272,304,368,464,496,550,650,736,836,
%T A083209 928,992,1184,1312,1376,1504,1696,1888,1952,2752,3008,3230,3392,3770,
%U A083209 3776,3904,4030,4288,4510,4544,4672,5056,5170,5312,5696,5830,6208,6464
%N A083209 Numbers with exactly one subset of their sets of divisors such that the complement has the same sum.
%C A083209 The weird numbers A006037 are not a subset of this sequence. The first missing weird number is A006037(8) = 10430.  [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 29 2009]
%C A083209 A083206(a(n))=1; perfect numbers (A000396) are a subset; problem: are weird numbers (A006037) a subset?
%H A083209 Alois P. Heinz, <a href="b083209.txt">Table of n, a(n) for n=1..100</a>
%H A083209 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PerfectNumber.html">Perfect Number.</a>
%H A083209 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/WeirdNumber.html">Weird Number.</a>
%H A083209 Reinhard Zumkeller, <a href="a083206.txt">Illustration of initial terms</a>
%e A083209 n=20: 2+4+5+10=1+20, 20 is a term (A083206(20)=1).
%p A083209 with (numtheory): b:= proc(n,l) option remember; local m, ll, i; m:= nops(l); if n<0 then 0 elif n=0 then 1 elif m=0 or add (i, i=l)<n then 0 else ll:= subsop (m=NULL, l); b(n, ll) +b(n-l[m], ll) fi end: a:= proc(n) option remember; local i, k, l, m, r; for k from `if`(n=1, 1, a(n-1)+1) do l:= sort ([divisors (k)[]]); m:= iquo (add (i, i=l), 2, 'r'); if r=0 and b(m, l)=2 then break fi od; k end: seq (a(n), n=1..30);  [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 29 2009]
%Y A083209 Cf. A005101, A005835, A064771.
%Y A083209 Adjacent sequences: A083206 A083207 A083208 this_sequence A083210 A083211 A083212
%Y A083209 Sequence in context: A094371 A079760 A109895 this_sequence A080714 A116368 A007622
%K A083209 nonn,new
%O A083209 1,1
%A A083209 Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 22 2003
%E A083209 More terms from  Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 29 2009

%I A155069
%S A155069 1,1,2,6,22,90,394,1806,8558,41586,206098,1037718,5293446,27297738,
%T A155069 142078746,745387038,3937603038,20927156706,111818026018,600318853926,
%U A155069 3236724317174,17518619320890,95149655201962,518431875418926
%N A155069 Expansion of (3-x-sqrt(1-6x+x^2))/2 in powers of x.
%C A155069 A minor variation of A006318. Unsigned version of A086456 and A103137. The Hankel transform of this sequence is A006125.
%F A155069 G.f.: (3-x-sqrt(1-6x+x^2))/2.
%Y A155069 Cf. A006318, A085403, A086456, A103137.
%K A155069 nonn,new
%O A155069 0,3
%A A155069 Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 02 2009

%I A154840
%S A154840 1,1,1,2,3,3,2,1,7,1,2,3,4,5,6,7,8,9,9,8,7,6,5,4,3,2,1,19,1,2,3,
%T A154840 4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,18,17,16,15,14,13,12,11,
%U A154840 10,9,8,7,6,5,4,3,2,1,37,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16
%N A154840 Distance to nearest cube different from n.
%C A154840 Equals A074989(n) if this is not zero, else 1+A055400(n-1), the distance to the nearest cube < n.
%e A154840 a(8)=7, because the two cubes below and above 8 are 1^3=1 and 3^3=27, and the distance to 1 is smaller, namely 8-1=7.
%p A154840 distNearstDiffCub := proc(n) local iscbr ; iroot(n,3,'iscbr') ; if iscbr then 1+A055400(n-1); else A074989(n) ; end if; end proc;
%Y A154840 Cf. A066635, A163497.
%K A154840 nonn,easy,new
%O A154840 0,4
%A A154840 R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 01 2009

%I A167404
%S A167404 1,1,1,1,2,1,2,1,2,1,1,3,1,2,1,3,2,3,3,2,1,2,1,4,1,3,2,1,1,4,2,4,4,3,2,
%T A167404 1,4,5,1,5,1,4,3,2,1,3,3,5,2,5,1,4,3,2,1,2,2,6,6,2,5,5,4,3,2,1,5,6,3,3,
%U A167404 6,6,1,5,4,3,2,1,1,1,7,1,7,2,6,1,5,4,3,2,1,6,7,4,7,3,7,2,6,6,5,4,3,2,1
%N A167404 Complete lower trim array of the Wythoff fractal sequence, A003603.
%C A167404 The lower trim sequence of a fractal sequence s is the fractal sequence
%C A167404 remaining after all 0s are deleted from the sequence s-1. Row n of A167404
%C A167404 consists of successive lower trim sequences beginning with A003603. Thus
%C A167404 every row is a fractal sequence. It is easy to prove that the combinatorial
%C A167404 limit or these rows is the sequence (1,2,3,4,5,6,...)=A000027.
%D A167404 Clark Kimberling, "Fractal sequences and interspersions," Ars Combinatoria 45 (1997) 157-168.
%e A167404 First five rows:
%e A167404 1 1 1 2 1 3 2 1 4 3 2 5 1 6 4 3 7 2 8 5 1 9 6 4 10 3 11 ... = A003603
%e A167404 1 2 1 3 2 1 4 5 3 2 6 1 7 4 8 5 3 9 2 10 6 1 11 7 4 12 .... = A167237
%e A167404 1 2 1 3 4 2 1 5 6 3 7 4 2 8 1 9 5 10 6 3 11 12 7 4 13 ...
%e A167404 1 2 3 1 4 5 2 6 3 1 7 8 4 9 5 2 10 11 6 3 12 1 13 7 14 ...
%e A167404 1 2 3 4 1 5 2 6 7 3 8 4 1 9 10 5 2 11 12 6 13 7 3 14 15 ...
%Y A167404 Cf. A003603, A167237, A035513.
%K A167404 nonn,tabl,new
%O A167404 1,5
%A A167404 Clark Kimberling (ck6(AT)evansville.edu), Nov 02 2009

%I A167153
%S A167153 10,12,14,16,18,20,22,24,26,28,31,33,35,37,39,41,43,45,47,50,52,54,56,
%T A167153 58,60,62,64,66,68,71,73,75,77,79,81,83,85,87,90,92,94,96,98,100,102,
%U A167153 104,106,108,110,112,114,116,118,120,122,124,126,128,130,132,134,136
%N A167153 Numbers not appearing in A167152.
%K A167153 nonn,new
%O A167153 1,1
%A A167153 Eric Angelini (Eric.Angelini(AT)kntv.be) and M. F. Hasler (MHasler(AT)univ-ag.fr), Nov 02 2009

%I A167152
%S A167152 1,2,3,4,5,6,7,8,9,11,29,13,49,15,69,17,89,19,199,21,399,23,599,25,799,
%T A167152 27,999,30,2999,3999,32,5999,34,7999,36,9999,38,29999,40,49999,42,69999,
%U A167152 44,89999,46,199999,48,399999,499999,51,699999,53,899999,55,1999999,57
%N A167152 Lexicographically first injective sequence such that a(n) = A007953(a(a(n))), where A007953 = sum of digits (in base 10).
%C A167152 "Lexicographically first" means that the sequence is constructed by choosing a(n) to be the smallest positive integer not leading to a contradiction, "injective" means that a number may occur only once, and is thereafter excluded from the possible choices for subsequent terms.
%C A167152 Open questions: (1) Prove that a(n)>n for all n>9.
%C A167152 (2) Prove that the subsequence of terms not ending in "9" is strictly increasing.
%C A167152 (3) Prove the given formula for a(n).
%C A167152 (4) Find an explicit formula for indices n where a(n)=m*10^k-1.
%H A167152 M. F. Hasler, <a href="b167152.txt">Table of n,a(n) for n=1,...,999</a>.
%H A167152 E. Angelini, <a href="http://www.cetteadressecomportecinquantesignes.com/Digitsum.htm">a(n) is the digitsum of a(a(n))</a>, November 2009.
%F A167152 If n < 10 or n is in { a(1),...,a(n-1) }, then a(n) = (n%9 + 1)*10^[n/9]-1 (=n for n<10).
%F A167152 Otherwise, a(n) = n+1 unless n+1 occurred earlier in the sequence (and therefore is of the from k*10^m-1), in which case a(n) = n+2 (conjectured).
%o A167152 (PARI) /* This code is for illustration and "experimental verification"; several important simplifications could be made to compute a(n) efficiently. */
%o A167152 A167152(n, output=0, u=[])={ my(a=vector(n),k); for( i=1+#u,#a, if( setsearch( u,i )
%o A167152 ,/* this index has already appeared, so this a(n) must have that digit sum */
%o A167152 k= ((i % 9)+1)*10^(i\9)-1; /* this k is the smallest number with digit sum i; this should work "at once" and the loop below should not be needed */
%o A167152 while( A007953(k) != i | setsearch(u, k), k+=10^(i\9-1)*9 /*e.g. to 89 we add 9*/)
%o A167152 ,/* index has not yet appeared : choose smallest number not yet used and not leading to contradiction */
%o A167152 /* is it possible that a[i] = k < i ? Clearly a[i] = i iff i <= 9, else digsum(i)<i. */
%o A167152 k=1; while( setsearch(u,k) | (k<=i & A007953(if( k<i, a[k], i)) != k), k++);
%o A167152 )/*end if i in u */;
%o A167152 output & if( #output>1, write(output,i" "k),print1(k,", ")); u=setunion( u, Set(a[i]=k))
%o A167152 )/* end for i */; k}
%K A167152 nonn,new
%O A167152 1,2
%A A167152 E. Angelini (Eric.Angelini(AT)kntv.be) and M. F. Hasler (MHasler(AT)univ-ag.fr), Nov 02 2009

%I A167403
%S A167403 1,3,10,35,126,462,1716,6435,24310,92368,352595,1351142,5194385,
%T A167403 20024980,77384340,299671971,1162635441,4518099300,17583582225,
%U A167403 68522664400,267350823015,1044243559263,4082760176300,15977236602150
%N A167403 Number of decimal numbers having n or fewer digits and having the sum of their digits equal to n.
%C A167403 a(3) = 10, because 10 decimal numbers have 3 or fewer digits and a digit sum of 3: 3, 30, 300, 12, 120, 201, 21, 210, 102, 111.
%p A167403 b:= proc(n,i) option remember; if n<0 or i<0 then 0 elif i=0 then `if` (n=0, 1, 0) elif n=0 then 1 else add (b(n-k, i-1), k=0..9) fi end: a:= n-> b(n, n): seq (a(n), n=1..30);
%Y A167403 Cf. A130835, A001700.
%K A167403 base,easy,nonn,new
%O A167403 1,2
%A A167403 Alois P. Heinz (heinz(AT)hs-heilbronn.de), Nov 02 2009

%I A131386
%S A131386 1,0,0,0,3,0,8,0,15,0,25,0,24,0
%V A131386 1,0,0,0,-3,0,8,0,-15,0,-25,0,24,0
%N A131386 Triangle read by rows: coefficients of polynomilas defined by B_0(X)=1, B_1(X)=X, B_2(X)=X^2+2, B_n(X)=XB_{n-1}(X)-B_{n-2}.
%C A131386 In the triangle the numbers are generated by the following formula B(i,j)=B(i-1,j)-B(i-2,j-1).
%H A131386 A. Belhadj, O. F. Onyango, N. Rozibaeva, <a href="http://pdf.aiaa.org/jaPreview/JTHT/2009/PVJA41850.pdf"></a>; J. of Thermophys. Heat Transf. 23 (2009) 639.
%H A131386 S. Fridjine , M. Amlouk, <a href="http://www.worldscinet.com/mplb/23/2317/S0217984909020321.html"></a>;Modern Phys. Lett. B 23 (2009) 2179.
%H A131386 S. Tabatabaei,T. Zhao, O. B. Awojoyogbe, F. Moses, <a href="http://www.springerlink.com/content/b125h6166r216313/"></a>;Heat Mass Transf. 45 (2009) 1247.
%F A131386 B(i,j)=B(i-1,j)-B(i-2,j-1)
%e A131386 The sequence is one of the lines of the triangle.
%K A131386 tabf,sign,new
%O A131386 1,5
%A A131386 Jamel Ghanouchi (jamel.ghanouchi(AT)topnet.tn), Aug 26 2008
%E A131386 Entry completely rewriten by Jamel Ghanouchi (jamel.ghanouchi(AT)topnet.tn), Nov 02 2009

%I A167402
%S A167402 0,0,4,12,44,116,356,948,2772,7396,20972,56108,156236,418228,1151556,
%T A167402 3081180,8421052,22514652,61207972,163518308,442769316,1181982628,
%U A167402 3190663628,8511628124,22920057932,61104234356,164212633412
%N A167402 Number of n-step walks on square lattice, self-avoiding until the last step.
%C A167402 A001411(n)=4^n-(a(n)+4*(a(n-1)+4*(a(n-2)+...)))
%F A167402 a(n) = 4*A001411(n-1)-A001411(n), n>0. [From Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 02 2009]
%Y A167402 See references given for A001411.
%K A167402 nonn,new
%O A167402 0,3
%A A167402 Vadim Sheikhman (vvsshh(AT)gmail.com), Nov 02 2009
%E A167402 More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 02 2009

%I A166505
%S A166505 202,203,205,207,302,303,305,502,505,507,702,703,705,707,1102,1105,1107,
%T A166505 1302,1305,1702,1703,1705,1707,1902,1903,1905,2002,2005,2007,2013,2019,
%U A166505 2022,2023,2025,2031,2032,2033,2035,2037,2041,2043,2047,2052,2055,2057
%N A166505 Numbers in A166504 which are not in A152242.
%C A166505 All terms have at least one zero digit and are composite,
%F A166505 a(n) = A166504(A166506(n))
%o A166505 (PARI) for(i=1,1e4, is_A166504(i) & !is_A152242(i) & print1(i", "))
%Y A166505 Cf. A152242, A166506 (indices of these terms in A166504).
%K A166505 nonn,new
%O A166505 1,1
%A A166505 M. F. Hasler (MHasler(AT)univ-ag.fr), Nov 02 2009

%I A167401
%S A167401 1,1,2,1,12,1,4,3,20
%N A167401 Smallest number a(n) so that n*a(n) has twice as many divisors as a(n)
%C A167401 a(n) is 1 for all prime numbers
%Y A167401 A139315
%K A167401 nonn,new
%O A167401 2,3
%A A167401 J. Lowell (jhbubby(AT)mindspring.com), Nov 02 2009

%I A166506
%S A166506 70,71,72,73,115,116,117,183,185,186,250,251,252,253,365,367,368,427,
%T A166506 429,534,535,536,537,594,595,596,640,6,42,643,645,647,648,649,650,653,
%U A166506 654,655,656,657,659,660,661,662,664,665,666,667,669,671,672,673,674
%N A166506 Indices of terms in A166504 which are not in A152242.
%F A166506 A166504(a(n)) = A166505(n).
%e A166506 a(1)=70 since the first term in A166504 which is not in A152242 is A166504(70)=202.
%o A166506 (PARI) c=0; for(i=1,1e4, is_A166504(i) & c++ & !is_A152242(i) & print1(c", "))
%Y A166506 Cf. A152242, A166504, A166505.
%K A166506 nonn,new
%O A166506 1,1
%A A166506 M. F. Hasler (MHasler(AT)univ-ag.fr), Nov 02 2009

%I A167400
%S A167400 2,1,1,8,8,4,4,1,1,111,88,67,55,42,32,23,15,6,3,2,2470,2022,1688,1358,
%T A167400 1119,880,702,520,393,268,189,122,87,57,48,33,24,11,6,1
%N A167400 Irregular triangle read by columns: frequency with which the value of the first subset member occurs in each subset of size N of the set {1..N^2}, whose members sum to a prime number.
%C A167400 The sequence is related to the method of subset construction, in which
%C A167400 the far left-hand member increases most slowly in value.
%C A167400 The.irregular.triangle.of.numbers.is:
%C A167400 First...........Frequency.with.which.the.value.of
%C A167400 Member..........the.first.subset.member.occurs
%C A167400 ..........N.....2..........3..........4..........5
%C A167400 .
%C A167400 .1..............2..........8........111.......2470
%C A167400 .2..............1..........8.........88.......2022
%C A167400 .3..............1..........4.........67.......1688
%C A167400 .4.........................4.........55.......1358
%C A167400 .5.........................1.........42.......1119
%C A167400 .6.........................1.........32........880
%C A167400 .7...................................23........702
%C A167400 .8...................................15........520
%C A167400 .9....................................6........393
%C A167400 10....................................3........268
%C A167400 11....................................2........189
%C A167400 12.............................................122
%C A167400 13..............................................87
%C A167400 14..............................................57
%C A167400 15..............................................48
%C A167400 16..............................................33
%C A167400 17..............................................24
%C A167400 18..............................................11
%C A167400 19...............................................6
%C A167400 20...............................................1
%C A167400 .
%C A167400 .Totals.........4.........26........444......11998
%e A167400 For N = 2, the subsets of {1, 2, 3, 4} whose members sum to primes are
%e A167400 {1, 2}, {1, 4}, {2, 3}, {3, 4}
%e A167400 The first member is 1 in 2 subsets, 2 in 1 subset and 3 in 1 subset,
%e A167400 giving the first 3 terms of the sequence: 2, 1, 1.
%Y A167400 A167147 = Column sums of the table above.
%K A167400 nonn,new
%O A167400 1,1
%A A167400 Christopher Hunt Gribble (chris.eveswell(AT)virgin.net), Nov 02 2009

%I A167399
%S A167399 0,1,2,2,6,10,20,28,59,162,218,497
%N A167399 a(n) = frequency with which each prime is the sum of the members of each subset of size N of the set {1..N^2} over N.
%Y A167399 Row sums of irregular triangle A167365.
%Y A167399 Cf. A167147 (Column sums of irregular triangle A167365.)
%K A167399 nonn,new
%O A167399 1,3
%A A167399 Christopher Hunt Gribble (chris.eveswell(AT)virgin.net), Nov 02 2009

%I A167397
%S A167397 1,21,34,43,48,61,72,75,80,87,102,115,118,143,148,151,156,193,204,213,
%T A167397 220,225,240,253,268,281,290,303,308,323,328,335,340,345,348,253,360,
%U A167397 363,370,399,402,407,414,423,434,441,444,451,454,459,490,495
%N A167397 n-th single (or isolated or non-twin) prime minus n.
%F A167397 a(n)=A007510(n)-A000027(n).
%e A167397 a(1)=2-1=1, a(2)=23-2=21, a(3)=37-3=34.
%Y A167397 Cf. A000027, A007510.
%K A167397 nonn,new
%O A167397 1,2
%A A167397 Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Nov 02 2009

%I A101288
%S A101288 1,5,6,7,5,5,4,2,2,3,3,4,9,6,7,10,12,10,12,13,15,26,27,30,36,41,43,46,
%T A101288 48,49,68,69,70,73
%N A101288 The number of primes between the n-th single or isolated prime and n-th single or isolated composite.
%e A101288 a(1)=1 (2<3<4); a(2)=5 (23>19&17&13&11&7>6); a(3)=6 (37>31&29&23&19&17&13>12).
%Y A101288 Cf. A000040, A007510, A014574.
%K A101288 nonn,new
%O A101288 1,2
%A A101288 Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Nov 02 2009

%I A167398
%S A167398 0,89,17711,3524578,701408733,139583862445,27777890035288,
%T A167398 5527939700884757,1100087778366101931,218922995834555169026,
%U A167398 43566776258854844738105,8670007398507948658051921
%N A167398 Fibonacci(11*n).
%F A167398 a(0)=0, a(1)=89; a(n>1)=199*a(n-1)+a(n-2).
%t A167398 (*1*)Table[Fibonacci[11k],{k,0,20}]
%t A167398 (*2*){a,b}={0,89};Do[Print[c={a,b}.{1,199}];a=b;b=c,{20}]
%Y A167398 Cf. A134498 Fibonacci(7n).
%K A167398 nonn,new
%O A167398 0,2
%A A167398 Zak Seidov (zakseidov(AT)yahoo.com), Nov 02 2009

%I A167395
%S A167395 4,30,42,60,60,72,102,102,102,102,138,138,138,180,180,180,180,228,228,
%T A167395 240,270,270,270,282,312,312,348,348,348,420,420,420,420,420,420,420,
%U A167395 420,420,420,462,462,462,462,522,522,522,522,522,522,522,570,570,570
%N A167395 Smallest single or isolated composite>nth single or isolated prime.
%Y A167395 Cf. A007510, A014574.
%K A167395 nonn,new
%O A167395 1,1
%A A167395 Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Nov 02 2009

%I A167394
%S A167394 2,2,2,2,23,37,47,67,97,97,131,131,173,173,173,211,233,263,277,307,337,
%T A167394 409,409,457,509,563,593,613,631,653,797,797,823,853,877,1013,1013,1039,
%U A167394 1039,1087,1129,1223,1259,1283,1297,1307,1423,1447,1471,1471,1601,1613
%N A167394 Largest single or isolated prime<nth single or isolated composite.
%Y A167394 Cf. A007510, A014574.
%K A167394 nonn,new
%O A167394 1,1
%A A167394 Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Nov 02 2009

%I A167390
%S A167390 1,3,7,10,19,24,40,46,71,78,114,122,171,181
%N A167390 Partial sums of A137442
%F A167390 Set R(N)=N+ROUND(SQRT(N),0), S(N)=FLOOR(SQRT(R(N))), U(N)=R(N)*(R(N)+1)/2-S(N)*(S(N)+1)*(S(N)+.5)/3, T(N)=CEILING(N/2), then a(N)=T(N)*(1+T(N)*(3+2*T(N)))/6+U(FLOOR(N/2))
%e A167390 a(14)=1+2+4+3+9+5+16+6+25+7+36+8+49+10=181
%K A167390 nonn,new
%O A167390 1,2
%A A167390 Gerald Hillier (adr.rabbicat(AT)gmail.com), Nov 02 2009

%I A167389
%S A167389 2,3,5,6,8,9,10,12,13,15,16,18,19,21,22,23,25,26,28,29,31,32,34,35,36,
%T A167389 38,39,41,42,44,45,47,48,49,51,52,54,55,57,58,60,61,62,64,65,67,68,70,
%U A167389 71,72,74,75,77,78,80,81,83,84,85,87,88,90,91,93,94,96,97,98,100,101
%N A167389 (argument(exp(-(ln(2)+W(n,-(1/2)*ln(2)))/ln(2)))*ln(2)+Im(W(n,-(1/2)*ln(2))))/(2*Pi*ln(2)) where W is the Lambert W function
%H A167389 <a href="http://mathworld.wolfram.com/LambertW-Function.html">Mathworld</a>
%H A167389 <a href="http://en.wikipedia.org/wiki/Lambert_W_function">Wikipedia</a>
%H A167389 <a href="http://www.orcca.on.ca/LambertW/">Poster</a>
%H A167389 <a href="http://kong.apmaths.uwo.ca/~rcorless/frames/PAPERS/LambertW/">RM Corless</a>
%F A167389 (argument(exp(-(ln(2)+W(n,-(1/2)*ln(2)))/ln(2)))*ln(2)+Im(W(n,-(1/2)*ln(2))))/(2*Pi*ln(2))
%p A167389 seq(round(evalf((argument(exp(-(ln(2)+LambertW(n, -(1/2)*ln(2)))/ln(2)))*ln(2)+Im(LambertW(n, -(1/2)*ln(2))))/(2*Pi*ln(2)))), n = 1 .. 100)
%K A167389 nonn,uned,new
%O A167389 1,1
%A A167389 Stephen Crowley (crow(AT)crowlogic.net), Nov 02 2009

%I A166504
%S A166504 2,3,5,7,11,13,17,19,22,23,25,27,29,31,32,33,35,37,41,43,47,52,53,55,57,
%T A166504 59,61,67,71,72,73,75,77,79,83,89,97,101,103,107,109,112,113,115,117,
%U A166504 127,131,132,133,135,137,139,149,151,157,163,167,172,173,175,177,179
%N A166504 Numbers which are the concatenation of primes, with "leading zeros" allowed.
%C A166504 A number is in this sequence iff it is prime or of the form a(k)*10^m+a(n), where a(k), a(n) are in this sequence and 10^m >= a(n) (and from this follows that one among a(k), a(n) can be taken to be prime).
%C A166504 This contains A152242 as a subsequence, but also additional terms like e.g. 202 which can be split into two primes, 2 and 02 (= 2). Such a splitting, where some of the substrings contain leading zeros, is not allowed in A152242.
%C A166504 Terms not in A152242 are listed in A166505.
%o A166504 (PARI) is_A166504(n)={ isprime(n) | ((bittest(n,0) | n%10==2) & for(i=1,#Str(n)-1, isprime(n%10^i) & is_A166504(n\10^i) & return(1)))}
%Y A166504 Cf. A152242.
%K A166504 nonn,new
%O A166504 1,1
%A A166504 M. F. Hasler (MHasler(AT)univ-ag.fr), Nov 02 2009

%I A167388
%S A167388 31,131,331,431,631,1031,1231,1531,1831,1931,2131,2531,2731,3331,3631,
%T A167388 3931,4231,4831,4931,5231,5431,5531,6131,7331,8231,8431,8731,8831,9431,
%U A167388 9631,9931,10331,10531,10631,10831,11131,11731,11831,13331,13831,13931
%N A167388 Prime numbers ending in the prime number 31
%K A167388 nonn,base,new
%O A167388 1,1
%A A167388 Mark A. Thomas (monstrousgaugetheory(AT)gmail.com), Nov 02 2009

%I A167387
%S A167387 1,0,2,0,10,0,35,0
%V A167387 1,0,-2,0,10,0,-35,0
%N A167387 The sequence is generated by a triangle generated by a Boubaker Polynomial which is defined as it follows B_0(X)=1, B_1(X)=X, B_2(X)=X^2+2, B_n(X)=XB_{n-1}(X)-B_{n-2}(X).
%C A167387 There is no formula but that of the triangle generated by Boubaker POlynomial B(i,j)=B(i-1,j)-B(i-2,j-1). See also A135929 and A138034 for further information.
%D A167387 A. Belhadj, O. F. Onyango, N. Rozibaeva, J. of Thermophys. Heat Transf. 23 (2009) 639.
%D A167387 S. Fridjine , M. Amlouk, Modern Phys. Lett. B 23 (2009) 2179.
%D A167387 S. Tabatabaei,T. Zhao, O. B. Awojoyogbe, F. Moses, Heat Mass Transf. 45 (2009) 1247.
%H A167387 <a href="http://pdf.aiaa.org/jaPreview/JTHT/2009/PVJA41850.pdf">Title?</a>
%H A167387 <a href="http://www.worldscinet.com/mplb/23/2317/S0217984909020321.html">Title?</a>
%H A167387 <a href="http://www.worldscinet.com/mplb/23/2317/S0217984909020321.html">Title?</a>
%F A167387 The sequence is one of the lines of the triangle defined by B(i,j)=B(i-1,j)-B(i-2,j-1).
%Y A167387 Cf. A138473, A138474, A138475, A138476, A138477, A138478, A138479.
%K A167387 sign,tabf,uned,new
%O A167387 1,3
%A A167387 Jamel Ghanouchi (jamel.ghanouchi(AT)topnet.tn), Nov 02 2009

%I A167386
%S A167386 1,0,1,0,2,0,10,0,25,0
%V A167386 1,0,-1,0,-2,0,10,0,-25,0
%N A167386 The sequence is one of the lines of a triangle generated by a Boubaker Polynomial whose definition is B_0(X)=1, B_1(X)=X, B_2(X)=X^2+2, B_n(X)=XB_{n-1}(X)-B_{n-2}(X).
%C A167386 The sequence may also be one of the lines of the triangle defined by B(i,j)=B(i-1,j)-B(i-2,j-1). See also A135929 and A138034 for further information.
%D A167386 A. Belhadj, O. F. Onyango, N. Rozibaeva, J. of Thermophys. Heat Transf. 23 (2009) 639.
%D A167386 S. Fridjine , M. Amlouk, Modern Phys. Lett. B 23 (2009) 2179.
%D A167386 S. Tabatabaei,T. Zhao, O. B. Awojoyogbe, F. Moses, Heat Mass Transf. 45 (2009) 1247.
%H A167386 <a href="http://pdf.aiaa.org/jaPreview/JTHT/2009/PVJA41850.pdf">Title?</a>
%H A167386 <a href="http://www.worldscinet.com/mplb/23/2317/S0217984909020321.html">Title?</a>
%H A167386 <a href="http://www.worldscinet.com/mplb/23/2317/S0217984909020321.html">Title?</a>
%F A167386 There is no formula, the only one is that of Boubaker Polynomial or of the triangle generated by the Polynomial.
%Y A167386 Cf. A138473, A138474, A138475, A138476, A138477, A138478, A138479.
%K A167386 sign,tabf,uned,new
%O A167386 1,5
%A A167386 Jamel Ghanouchi (jamel.ghanouchi(AT)topnet.tn), Nov 02 2009

%I A167385
%S A167385 1,3,5,8,12,17,24,33,45,61,82,110,147,196,261,347,461,612,812,1077,1428,
%T A167385 1893,2509,3325,4406,5838,7735,10248,13577,17987,23829
%N A167385 Offset sum sequence of A000931: g[n]=Sum[A000931[i+3],{i,0,n}]
%C A167385 The limiting ratio:
%C A167385 g[n+1]/g[n]->the minimal Pisot 1.3247179572447463...
%t A167385 Clear[f, g, n]
%t A167385 f[0] = 0; f[1] = 1; f[2] = 1; f[n_] := f[n] = f[n - 2] + f[n - 3];
%t A167385 g[n_] := Sum[f[i + 3], {i, 0, n}]
%t A167385 Table[g[n], {n, 0, 30}]
%K A167385 nonn,uned,new
%O A167385 0,2
%A A167385 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 02 2009

%I A167384
%S A167384 1,3,5,6,9,10,13,14,17,18,21,22,23,27,28,29,33,34,35,39,40,41,45,46,47,
%T A167384 51,52,53,57,58,59,60,65,66,67,68,73,74,75,76,81,82,83,84,89,90,91,92,
%U A167384 97,98,99,100
%N A167384 Numeral numbers shared in two parts. Take A000027 in even squares 4,16,36,64,100,144,=A016742(n+1); consider array with row 1: 1,2; row 2: 3,4; row 3: 5,6,7,8; row 4: 9,10,11,12; 1,2 and 3,4 beeing in central columns. Number of terms is 2,2,4,4,4,4,6,6,6,6,6,6,=A001670. Left part is a(n).
%C A167384 See submitted A167381. (Other possibility is reversal a(n) ie ra(n)=1,3,6,5,10,9,14,13,18,17,23,). Right part or companion is b(n)=2,4,7,8,11,12,15,16,19,20,24,.
%Y A167384 A112649.
%K A167384 nonn,uned,new
%O A167384 0,2
%A A167384 Paul Curtz (bpcrtz(AT)free.fr), Nov 02 2009

%I A167383
%S A167383 0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,4,4,4,4,5,
%T A167383 5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,8,9,9,9,10,10,11,11,11,11,11,11,12,13,13,
%U A167383 14,15,15,15,16,16,16,17,17,18,18,19,19,19,19,20,20,20,21,21,21,21,22
%N A167383 Entropy like stair step sequence based on A008185: a(n)=a(n-1)+Ceiling[ -(A008185[n + 2]/A008185[n + 1])*Log[(A008185[n + 2]/A008185[n + 1])]/Log[2]]
%C A167383 By using the ratio:
%C A167383 A008185[n + 2]/A008185[n + 1]
%C A167383 the sequence gets a probability effect that gives
%C A167383 a devil's staircase like result.
%F A167383 a(n)=a(n-1)+Ceiling[ -(A008185[n + 2]/A008185[n + 1])*Log[(A008185[n + 2]/A008185[n + 1])]/Log[2]]
%t A167383 Clear[f, g, n]; f[0] = 1; f[1] = 1; f[2] = 1;
%t A167383 f[n_] := f[n] = f[n - f[n - 1]] + f[n - f[n - 2]];
%t A167383 g[0] = 0; g[1] = 1;
%t A167383 g[n_] := g[n] = g[n - 1] + Ceiling[ -(f[n + 2]/f[n + 1])*Log[(f[n + 2]/f[n + 1])]/Log[2]]
%t A167383 a = Table[g[n], {n, 0, 200}]
%Y A167383 A008185, A136640
%K A167383 nonn,uned,new
%O A167383 0,15
%A A167383 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 02 2009

%I A167382
%S A167382 1,0,0,0,3,0,8,0,15,0,25,0,24,0
%V A167382 1,0,0,0,-3,0,8,0,-15,0,-25,0,24,0
%N A167382 The sequence is generated by a triangle, himself generated by Boubaker Polynomial as follows B_0(X)=1, B_1(X)=X, B_2(X)=X^2+2, B_n(X)=XB_{n-1}(X)-B_{n-2}.
%C A167382 See A135929 and A138034 for further information.
%D A167382 S. Tabatabaei,T. Zhao, O. B. Awojoyogbe, F. Moses, Heat Mass Transf. 45 (2009) 1247.
%D A167382 A. Belhadj, O. F. Onyango, N. Rozibaeva, J. of Thermophys. Heat Transf. 23 (2009) 639.
%D A167382 S. Fridjine , M. Amlouk, Modern Phys. Lett. B 23 (2009) 2179.
%H A167382 <a href="http://pdf.aiaa.org/jaPreview/JTHT/2009/PVJA41850.pdf">Title?</a>
%H A167382 <a href="http://www.worldscinet.com/mplb/23/2317/S0217984909020321.html">Title?</a>
%H A167382 <a href="http://www.worldscinet.com/mplb/23/2317/S0217984909020321.html">Title?</a>
%F A167382 B(i,j)=B(i-1,j)-B(i-2,j-1). The sequence is one of the lines of the triangle.
%Y A167382 Cf. A138473, A138474, A138475, A138476, A138477, A138478, A138479.
%K A167382 sign,tabf,uned,new
%O A167382 1,5
%A A167382 Jamel Ghanouchi (jamel.ghanouchi(AT)topnet.tn), Nov 02 2009

%I A167381
%S A167381 1,3,6,10,14,18,23,29,35,41,47,53,60,68,76,84,92,100,108,116,125,135,
%T A167381 145,155,165,175,185,195,205,215
%N A167381 Take naturals A000027 in successive even squares 4,16,36,64,=A016742(n+1). Corresponding array is chosen symmetric. Then left and right parts.First of central two columns (or first of left part) is a(n).
%C A167381 4,16,36,64 which sum is 120 ,like Janet 8*32 table, is also beginning of differences of 1,5,21,57,121,221,=A166464 from Janet form. Columns will be numbered 1,3,5, for left part (from right to left) and 2,4,6, for right part. Note possibily to consider squares in "Janet form" i.e. sequence must be considered from right to left.Hence (again) permutation of A000027: 2,1,4,3,8,7,6,5,12,11,10,9,16,15,14,13,20,19,18,17,26,25,24,23,22,21,32,.(See A166133). In both cases,rows have 2,2,4,4,4,4,6,6,6,6,6,6,8,8,8,8,8,8,8,8,10,=A001670 terms. a(n) differences:2,3,4,4,4,5,6,6,6,6,6,7,.
%Y A167381 A113127, A145913.
%K A167381 nonn,uned,new
%O A167381 0,2
%A A167381 Paul Curtz (bpcrtz(AT)free.fr), Nov 02 2009

%I A167380
%S A167380 1,2,4,5,1,4,5,1,4,5,1,4,5,4,5,1,4,5,4,5,1,4,5
%V A167380 1,2,4,5,1,-4,-5,-1,4,5,1,-4,-5,4,5,1,-4,-5,4,5,1,-4,-5
%N A167380 a(1)=1, a(2)=2, a(6k-3)=4, a(6k-2)=5, a(6k-1)=1, a(6k)=-4, a(6k+1)=-5, a(6k+2)=-1
%D A167380 A. Belhadj, O. F. Onyango, N. Rozibaeva, J. of Thermophys. Heat Transf. 23 (2009) 639.
%D A167380 S. Fridjine , M. Amlouk, Modern Phys. Lett. B 23 (2009) 2179.
%D A167380 S. Tabatabaei,T. Zhao, O. B. Awojoyogbe, F. Moses, Heat Mass Transf. 45 (2009) 1247.
%H A167380 <a href="http://www.springerlink.com/content/b125h6166r216313">Title?</a>
%H A167380 <a href="http://pdf.aiaa.org/jaPreview/JTHT/2009/PVJA41850.pdf">Title?</a>
%H A167380 <a href="http://www.worldscinet.com/mplb/23/2317/S0217984909020321.html">Title?</a>
%F A167380 a(1)=1, a(2)=2, a(6k-3)=4, a(6k-2)=5, a(6k-1)=1, a(6k)=-4, a(6k+1)=-5, a(6k+2)=-1
%Y A167380 Cf. A138473, A138474, A138475, A138476, A138477, A138478, A138479.
%K A167380 sign,tabf,uned,new
%O A167380 1,2
%A A167380 Jamel Ghanouchi (jamel.ghanouchi(AT)topnet.tn), Nov 02 2009

%I A167379
%S A167379 2,4,6,10,14,20,24,34,36,46,50,60,64,66,76,80,90
%N A167379 Let p and q be twin primes, excluding the pair (3,5). Then p+q is always divisible by 6 and we set a(n) = (p+q)/6.
%Y A167379 Cf. A002822 [From Zak Seidov, Nov 02 2009]
%K A167379 nonn,new,more
%O A167379 1,1
%A A167379 Tanin (Mirza Sabbir Hossain Beg) (mirzasabbirhossainbeg(AT)yahoo.com), Nov 02 2009
%E A167379 Edited (but not checked) by njas, Nov 02 2009

%I A167375
%S A167375 1,3,11,30,79,207,542,1419,3715,9726,25463,66663
%N A167375 The sequence is B_n, with B_0=1, B_1=3, B_2=11, B_n=3B_{n-1}-B_{n-2}.
%C A167375 B_n is in fact B_n(X=3) a Boubaker Polynomial for X=3.
%H A167375 A. Belhadj, O. F. Onyango, N. Rozibaeva, <a href="http://pdf.aiaa.org/jaPreview/JTHT/2009/PVJA41850.pdf">Title?</a> J. of Thermophys. Heat Transf. 23 (2009) 639.
%H A167375 S. Fridjine , M. Amlouk, <a href="http://www.worldscinet.com/mplb/23/2317/S0217984909020321.html">Title?</a>Modern Phys. Lett. B 23 (2009) 2179.
%H A167375 S. Tabatabaei,T. Zhao, O. B. Awojoyogbe, F. Moses, <a href="http://www.springerlink.com/content/b125h6166r216313/">Title?</a>Heat Mass Transf. 45 (2009) 1247.
%F A167375 B_3=1, B_1=3, B_2=11, B_n=3B_{n-1}-B_{n-2}
%Y A167375 A138473, A138474, A138475, A138476, A138477, A138478, A138479.
%K A167375 sign,tabf,uned,new
%O A167375 1,2
%A A167375 Jamel Ghanouchi (jamel.ghanouchi(AT)topnet.tn), Nov 02 2009

%I A167374
%S A167374 1,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,
%T A167374 0,0,1,1,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,1,
%U A167374 1,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1,1
%V A167374 1,-1,1,0,-1,1,0,0,-1,1,0,0,0,-1,1,0,0,0,0,-1,1,0,0,0,0,0,-1,1,0,0,0,0,
%W A167374 0,0,-1,1,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,-1,
%X A167374 1,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,-1,1
%N A167374 Triangle , read by rows, given by [ -1,1,0,0,0,0,0,0,0,...] DELTA [1,0,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938.
%C A167374 Riordan array (1-x,1) read by rows ; riordan inverse is (1/(1-x),1) .Columns have g.f. (1-x)x^k . Diagonal sums are A033999. Unsigned version in A097806.
%F A167374 Sum_{k, 0<=k<=n} T(n,k)*x^k = A000007(n), A011782(n), A025192(n), A002001(n), A005054(n), A052934(n), A055272(n), A055274(n), A055275(n), A055268(n), A055276(n) for x = 1,2,3,4,5,6,7,8,9,10,11 respectively .
%e A167374 Triangle begins : 1 ; -1,1 ; 0,-1,1 ; 0,0,-1,1 ; 0,0,0,-1,1 ; 0,0,0,0,-1,1 ; ...
%K A167374 sign,tabl,new
%O A167374 0,1
%A A167374 Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 02 2009

%I A167201
%S A167201 5,14,21,28,70,56,48,162,216,120
%N A167201 Third in a series of triangular subarrays of A117506. Previous arrays are Tables A007318 and A059797.
%C A167201 This subarray is generated from values related to the source partition 3+3. (cf A161924).
%e A167201 The domain values begin:
%e A167201 12
%e A167201 20..25
%e A167201 36..41..51
%e A167201 68..73..83..103
%e A167201 so based on function A117506, a(n) begins:
%e A167201 5
%e A167201 14..21
%e A167201 28..70..56
%e A167201 48..162..216..120
%e A167201 Note that A117506(22) maps to Partition 3+3
%e A167201 which corresponds to the 12th natural number appearing in A161924.
%Y A167201 A007318 A099627 A117506 A161924
%K A167201 more,nonn,tabl,new
%O A167201 1,1
%A A167201 Alford Arnold (Alford1940(AT)aol.com), Nov 02 2009

%I A167373
%S A167373 1,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,
%T A167373 2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,3,1,2,3
%V A167373 1,3,-1,-2,3,-1,-2,3,-1,-2,3,-1,-2,3,-1,-2,3,-1,-2,3,-1,-2,3,-1,-2,3,-1,
%W A167373 -2,3,-1,-2,3,-1,-2,3,-1,-2,3,-1,-2,3,-1,-2,3,-1,-2,3,-1,-,3,-1,-2,3
%N A167373 This sequence is generated from a triangle himself generated from a Boubaker Polynomials B_n(X). This one is described as B_0(X)=1, B_1(X)=X, B_2(X)=X^2+2, B_n(X)=XB_{n-1}(X)-B_{n-2}(X). The sequence is equal to B_{2k-1}(1) for k=1 to infinity.
%C A167373 The sequence is also the sum of the terms of the odd lines of the triangle generated by a Boubaker Polynomial.
%D A167373 M. Abramovitz and I. A. Stegun, eds., Handbook of Mathematical functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972, Chapter 22.
%D A167373 Planet Math, Boubaker Polynomials.
%H A167373 <a href="http://planetmath.org/encyclopedia/BoubakerPolynomials.html">Boubaker Polynomials</a>
%F A167373 a(1)=1, a(2)=3, a(3)=-1, a(4)=-2, a(5)=3, a(3k)=-1, a(3k+1)=-2, a(3k+2)=3.
%Y A167373 Cf. A138473, A138474, A138475, A138476, A138477, A138478, A138479.
%K A167373 sign,tabf,uned,new
%O A167373 1,2
%A A167373 Jamel Ghanouchi (jamel.ghanouchi(AT)topnet.tn), Nov 02 2009

%I A167372
%S A167372 5,7,11,5,13,7,17,7,37,19,29,119,47,41,23,5,29,31,37,11,37,41,43,13,7,
%T A167372 13,71,13,49,13,7
%N A167372 A120301(A123944(n))/A058313(A123944(n))
%C A167372 A123944(n) = {19, 28, 87, 99, 104, 196, 203, 210, 222, 228, 231, 238, 281, 328, 367, 499, 579, 620, 888, 967, 1036, 1147, 1204, 1352, 1372, 1403, 1419, 1430, 1470, ...} Numbers n such that A120301(n) differs from A058313(n).
%C A167372 A120301(n) = {1, 1, 5, 7, 47, 37, 319, 533, 1879, 1627, 20417, 18107, 263111, 237371, 52279, 95549, 1768477, 1632341, 167324635, 155685007, ...} Absolute value of numerator of the sum of all matrix elements of n X n matrix M[i,j] = (-1)^(i+j) * i/j, (i,j=1..n).
%C A167372 A058313(n) = {1, 1, 5, 7, 47, 37, 319, 533, 1879, 1627, 20417, 18107, 263111, 237371, 52279, 95549, 1768477, 1632341, 33464927, 155685007, ...} Numerator of the n-th alternating harmonic number, sum ((-1)^(k+1)/k, k=1..n).
%C A167372 The ratio A120301(n)/A058313(n) = 1 for most n.
%C A167372 a(n) is prime for most n.
%C A167372 The first composite ratio a(12) = 119 = 7*17 corresponds to A123944(12) = 238.
%C A167372 Next two composite a(n) = 49 = 7^2 correspond to A123944 = 1470 and A123944 = 10290.
%t A167372 f=0; Do[f=f+(-1)^(n+1)*1/n; g=Abs[(2(-1)^n*n+(-1)^n-1)/4]*f; rfg=Numerator[g]/Numerator[f]; If[(rfg==1)==False, Print[rfg]], {n, 1, 1500}]
%Y A167372 Cf. A123944, A120301, A058313.
%K A167372 more,nonn,new
%O A167372 1,1
%A A167372 Alexander Adamchuk (alex(AT)kolmogorov.com), Nov 02 2009

%I A167371
%S A167371 1,0,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,0,1,
%T A167371 1,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,
%U A167371 0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1
%N A167371 Triangle, read by rows, given by [0,1,-1,0,0,0,0,0,0,0,0,...] DELTA [1,0,-1,1,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938.
%C A167371 Diagonal sums : A060576 .
%F A167371 Sum_{k, 0<=k<=n}T(n,k)*x^k = A000007(n), A046698(n+1), A111286(n+1), A027327(n) for x= 0, 1, 2, 3 respectively.
%e A167371 Rows begin : [1}, {0, 1}, {0, 1, 1}, {0, 0, 1, 1}, {0, 0, 0, 1, 1}, {0, 0, 0, 0, 1, 1}, ...
%Y A167371 Cf. A097806, A103451
%K A167371 nonn,tabl,new
%O A167371 0,1
%A A167371 Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 02 2009

%I A167369
%S A167369 1,5,47450,1333735856351858432985890996140258
%N A167369 sigma(n!,n!).
%t A167369 Array[DivisorSigma[ #!,#! ]&,5,1]
%Y A167369 Cf. A062569, A167367, A167368
%K A167369 nonn,new
%O A167369 1,2
%A A167369 Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 01 2009

%I A167366
%S A167366 1,3,1,2,1,1,2,2,3,1,2,0,0,1,1,2,2,0,0,3,1,2,0,2,0,2,1,1,2,2,2,2,2,2,3,
%T A167366 1,2,0,0,0,0,0,0,1,1,2,2,0,0,0,0,0,0,3,1,2,0,2,0,0,0,0,0,2,1,1,2,2,2,2,
%U A167366 0,0,0,0,2,2,3,1,2,0,0,0,2,0,0,0,2,0,0,1,1
%N A167366 Triangle by rows, 2*A047999 - A097806 (signed) = twice Sierpinski's gasket - the signed pair sum operator.
%C A167366 Row sums = A167275: (1, 4, 4, 8, 4, 8, 8, 16,...).
%F A167366 Triangle by rows, 2*A047999 - A096806, the pair sum operator.
%F A167366 A096806 is signed, rightmost diagonal = (+,+,+,...); adjacent diagonal is
%F A167366 signed (-,-,-,...).
%e A167366 First few rows of the triangle =
%e A167366 1;
%e A167366 3, 1;
%e A167366 2, 1, 1;
%e A167366 2, 2, 3, 1;
%e A167366 2, 0, 0, 1, 1;
%e A167366 2, 2, 0, 0, 3, 1;
%e A167366 2, 0, 2, 0, 2, 1, 1;
%e A167366 2, 2, 2, 2, 2, 2, 3, 1;
%e A167366 2, 0, 0, 0, 0, 0, 0, 1, 1;
%e A167366 2, 2, 0, 0, 0, 0, 0, 0, 3, 1;
%e A167366 2, 0, 2, 0, 0, 0, 0, 0, 2, 1, 1;
%e A167366 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 3, 1;
%e A167366 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 1, 1;
%e A167366 2, 2, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 3, 1;
%e A167366 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 1, 1;
%e A167366 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 1;
%e A167366 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1;
%e A167366 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 1;
%e A167366 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1;
%e A167366 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 3, 1;
%e A167366 ...
%Y A167366 Cf. A047999, A097806
%K A167366 nonn,tabl,new
%O A167366 0,2
%A A167366 Gary W. Adamson & Mats Granvik (qntmpkt(AT)yahoo.com), Nov 01 2009

%I A167368
%S A167368 1,3,12,159120,6686252969760,
%T A167368 89050715142739003008099466232718435351438398888454549774336000,
%U A167368 9145596818846150507718884713380452019693379773183410407022915926142348385998637390964345055065925108019866601520875494114267750747052992798443506679109586039865344000000
%N A167368 sigma(n!!!).
%t A167368 Array[DivisorSigma[1,#!! ]&,7,1]
%Y A167368 Cf. A062569, A167367
%K A167368 nonn,new
%O A167368 1,2
%A A167368 Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 01 2009

%I A167367
%S A167367 1,3,4,15,24,124,192,1020,1920,12264,23040,159666,322560,2555280,
%T A167367 5041344,40893840,90744192,761260368,1814883840,15732804296,38900010240,
%U A167367 377587663200,933600245760,9087075973248,23520702965760,254438142416640
%N A167367 sigma(n!!).
%t A167367 Array[DivisorSigma[1,#!! ]&,50,1]
%Y A167367 Cf. A062569
%K A167367 nonn,new
%O A167367 1,2
%A A167367 Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 01 2009

%I A167364
%S A167364 1,0,1,1,1,0,0,0,0,1,1,0,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,0,0,0,0,0,0,0,
%T A167364 1,1,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,1,0,0,1,1,0,0,0,0,0,1,0,0,1,0,0,0,1,
%U A167364 0,0,0,1,0,0,0,0
%N A167364 Triangle by rows, A047999 * A010060 (diagonalized); as infinite lower triangular matrices.
%C A167364 Row sums = A048896: (1, 1, 2, 1, 2, 2, 4, 1, 2, 2, 4,...). Right border = Thue-Morse sequence A010060, starting with offset 1.
%F A167364 Let S = Sierpinski's gasket, A047999. Let Q = a diagonalized version of the
%F A167364 Thue-Morse sequence, A010060: [0; 0,1; 0,0,1; 0,0,0,0; 0,0,0,0,1;...], (i.e.
%F A167364 A010060 as the rightmost diagonal and the rest zeros).
%F A167364 A167364 = S * Q, as infinite lower triangular matrices. Delete leftmost
%F A167364 column of zeros.
%e A167364 First few rows of the triangle =
%e A167364 1;
%e A167364 0, 1;
%e A167364 1, 1, 0;
%e A167364 0, 0, 0, 1;
%e A167364 1, 0, 0, 1, 0;
%e A167364 0, 1, 0, 1, 0, 0;
%e A167364 1, 1, 0, 1, 0, 0, 1;
%e A167364 0, 0, 0, 0, 0, 0, 0, 1;
%e A167364 1, 0, 0, 0, 0, 0, 0, 1, 0;
%e A167364 0, 1, 0, 0, 0, 0, 0, 1, 0, 0;
%e A167364 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1;
%e A167364 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0
%e A167364 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1;
%e A167364 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1;
%e A167364 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0;
%e A167364 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1
%e A167364 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0;
%e A167364 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0;
%e A167364 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1;
%e A167364 ...
%Y A167364 Cf. A047999, A010060
%K A167364 nonn,tabl,new
%O A167364 1,1
%A A167364 Gary W. Adamson & Mats Granvik (qntmpkt(AT)yahoo.com), Nov 01 2009

%I A167365
%S A167365 0,1,2,1,0,0,0,1,5,7,7,5,1,0,0,0,0,1,3,11,18,38,71,79,79,61,50,27,6,0,0,
%T A167365 0,0,0,2,5,18,70,101,253,409,502,710,1038,1297,1350,1383,1297,1225,931,
%U A167365 710,409,141,70,47,18,10,2
%N A167365 Irregular triangle read by columns: Frequency with which different primes result from the sum of the members of each subset of size N of the set {1..N^2}.
%C A167365 The irregular triangle of numbers is:
%C A167365 .
%C A167365 .Prime...Prime...........Frequency.with.which.different.prime
%C A167365 .Index...................sums.occur
%C A167365 ..................N......2..........3..........4..........5
%C A167365 .
%C A167365 ..1........2.............0..........0..........0..........0
%C A167365 ..2........3.............1..........0..........0..........0
%C A167365 ..3........5.............2..........0..........0..........0
%C A167365 ..4........7.............1..........1..........0..........0
%C A167365 ..5.......11........................5..........1..........0
%C A167365 ..6.......13........................7..........3..........0
%C A167365 ..7.......17........................7.........11..........2
%C A167365 ..8.......19........................5.........18..........5
%C A167365 ..9.......23........................1.........38.........18
%C A167365 .10.......29..................................71.........70
%C A167365 .11.......31..................................79........101
%C A167365 .12.......37..................................79........253
%C A167365 .13.......41..................................61........409
%C A167365 .14.......43..................................50........502
%C A167365 .15.......47..................................27........710
%C A167365 .16.......53...................................6.......1038
%C A167365 .17.......59...........................................1297
%C A167365 .18.......61...........................................1350
%C A167365 .19.......67...........................................1383
%C A167365 .20.......71...........................................1297
%C A167365 .21.......73...........................................1225
%C A167365 .22.......79............................................931
%C A167365 .23.......83............................................710
%C A167365 .24.......89............................................409
%C A167365 .25.......97............................................141
%C A167365 .26......101.............................................70
%C A167365 .27......103.............................................47
%C A167365 .28......107.............................................18
%C A167365 .29......109.............................................10
%C A167365 .30......113..............................................2
%C A167365 .
%C A167365 .Totals..................4.........26........444......11998
%e A167365 If N = 2 then there are 4 subsets of set {1,2,3,4} with prime sums:
%e A167365 .Subset..Sum
%e A167365 .{1,2}....3
%e A167365 .{1,4}....5
%e A167365 .{2,3}....5
%e A167365 .{3,4}....7
%e A167365 These sums can be represented by:
%e A167365 .Prime...Prime...Freq
%e A167365 .Index
%e A167365 .1.........2.......0
%e A167365 .2.........3.......1
%e A167365 .3.........5.......2
%e A167365 .4.........7.......1
%e A167365 The numbers under Freq give the first 4 terms of the sequence.
%Y A167365 A167147 = Column sums of the table above.
%K A167365 nonn,new
%O A167365 1,3
%A A167365 Christopher Hunt Gribble (chris.eveswell(AT)virgin.net), Nov 01 2009

%I A167363
%S A167363 1,25,36,625,64,900,100,15625,1296,1600,196,22500,256,2500,2304,390625,
%T A167363 400,32400,484,40000,3600,4900,676,562500,4096,6400,46656,62500,1024,
%U A167363 57600,1156,9765625,7056,10000,6400,810000,1600,12100,9216,1000000,1936
%N A167363 Totally multiplicative sequence with a(p) = (p+3)^2 = p^2+6p+9 for prime p.
%F A167363 Multiplicative with a(p^e) = ((p+3)^2)^e. If n = Product p(k)^e(k) then a(n) = Product ((p(k)+3)^2)^e(k). a(n) = A166591(n)^2.
%K A167363 nonn,new
%O A167363 1,2
%A A167363 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167362
%S A167362 1,5,0,25,16,0,40,125,0,80,112,0,160,200,0,625,280,0,352,400,0,560,
%T A167362 520,0,256,800,0,1000,832,0,952,3125,0,1400,640,0,1360,1760,0,2000,
%U A167362 1672,0,1840,2800,0,2600,2200,0,1600,1280
%V A167362 1,-5,0,25,16,0,40,-125,0,-80,112,0,160,-200,0,625,280,0,352,400,0,-560,
%W A167362 520,0,256,-800,0,1000,832,0,952,-3125,0,-1400,640,0,1360,-1760,0,-2000,
%X A167362 1672,0,1840,2800,0,-2600,2200,0,1600,-1280
%N A167362 Totally multiplicative sequence with a(p) = (p-3)*(p+3) = p^2-9 for prime p.
%F A167362 Multiplicative with a(p^e) = ((p-3)*(p+3))^e. If n = Product p(k)^e(k) then a(n) = Product ((p(k)-3)*(p(k)+3))^e(k). a(n) = A166589(n) * A166591(n).
%K A167362 nonn,new
%O A167362 1,2
%A A167362 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167361
%S A167361 1,1,0,1,4,0,16,1,0,4,64,0,100,16,0,1,196,0,256,4,0,64,400,0,16,100,0,
%T A167361 16,676,0,784,1,0,196,64,0,1156,256,0,4,1444,0,1600,64,0,400,1936,0,256,
%U A167361 16
%N A167361 Totally multiplicative sequence with a(p) = (p-3)^2 = p^2-6p+9 for prime p.
%F A167361 Multiplicative with a(p^e) = ((p-3)^2)^e. If n = Product p(k)^e(k) then a(n) = Product ((p(k)-3)^2)^e(k). a(3k) = 0 for k >= 1. a(n) = A166589(n)^2.
%K A167361 nonn,new
%O A167361 1,5
%A A167361 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167360
%S A167360 1,20,30,400,56,600,90,8000,900,1120,182,12000,240,1800,1680,160000,380,
%T A167360 18000,462,22400,2700,3640,650,240000,3136,4800,27000,36000,992,33600,
%U A167360 1122,3200000,5460,7600,5040,360000,1560,9240,7200,448000,1892,54000
%N A167360 Totally multiplicative sequence with a(p) = (p+2)*(p+3) = p^2+5p+6 for prime p.
%F A167360 Multiplicative with a(p^e) = ((p+2)*(p+3))^e. If n = Product p(k)^e(k) then a(n) = Product ((p(k)+2)*(p(k)+3))^e(k). a(n) = A166590(n) * A166591(n).
%K A167360 nonn,new
%O A167360 1,2
%A A167360 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167359
%S A167359 1,4,0,16,14,0,36,64,0,56,104,0,150,144,0,256,266,0,336,224,0,416,
%T A167359 500,0,196,600,0,576,806,0,924,1024,0,1064,504,0,1326,1344,0,896,
%U A167359 1634,0,1800,1664,0,2000,2156,0,1296,784
%V A167359 1,-4,0,16,14,0,36,-64,0,-56,104,0,150,-144,0,256,266,0,336,224,0,-416,
%W A167359 500,0,196,-600,0,576,806,0,924,-1024,0,-1064,504,0,1326,-1344,0,-896,
%X A167359 1634,0,1800,1664,0,-2000,2156,0,1296,-784
%N A167359 Totally multiplicative sequence with a(p) = (p+2)*(p-3) = p^2-p-6 for prime p.
%F A167359 Multiplicative with a(p^e) = ((p+2)*(p-3))^e. If n = Product p(k)^e(k) then a(n) = Product ((p(k)+2)*(p(k)-3))^e(k). a(3k) = 0 for k >= 1. a(n) = A166590(n) * A166589(n).
%K A167359 nonn,new
%O A167359 1,2
%A A167359 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167358
%S A167358 1,16,25,256,49,400,81,4096,625,784,169,6400,225,1296,1225,65536,361,
%T A167358 10000,441,12544,2025,2704,625,102400,2401,3600,15625,20736,961,19600,
%U A167358 1089,1048576,4225,5776,3969,160000,1521,7056,5625,200704,1849,32400
%N A167358 Totally multiplicative sequence with a(p) = (p+2)^2 = p^2+4p+4 for prime p.
%F A167358 Multiplicative with a(p^e) = ((p+2)^2)^e. If n = Product p(k)^e(k) then a(n) = Product ((p(k)+2)^2)^e(k). a(n) = A166590(n)^2.
%K A167358 nonn,new
%O A167358 1,2
%A A167358 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167357
%S A167357 1,0,6,0,24,0,50,0,36,0,126,0,176,0,144,0,300,0,374,0,300,0,546,0,576,0,
%T A167357 216,0,864,0,986,0,756,0,1200,0,1400,0,1056,0,1716,0,1886,0,864,0,2250,
%U A167357 0,2500,0
%N A167357 Totally multiplicative sequence with a(p) = (p-2)*(p+3) = p^2+p-6 for prime p.
%F A167357 Multiplicative with a(p^e) = ((p-2)*(p+3))^e. If n = Product p(k)^e(k) then a(n) = Product ((p(k)-2)*(p(k)+3))^e(k). a(2k) = 0 for k >= 1. a(n) = A166586(n) * A166591(n).
%K A167357 nonn,new
%O A167357 1,3
%A A167357 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167356
%S A167356 1,0,0,0,6,0,20,0,0,0,72,0,110,0,0,0,210,0,272,0,0,0,420,0,36,0,0,0,702,
%T A167356 0,812,0,0,0,120,0,1190,0,0,0,1482,0,1640,0,0,0,1980,0,400,0
%N A167356 Totally multiplicative sequence with a(p) = (p-2)*(p-3) = p^2-5p+6 for prime p.
%F A167356 Multiplicative with a(p^e) = ((p-2)*(p-3))^e. If n = Product p(k)^e(k) then a(n) = Product ((p(k)-2)*(p(k)-3))^e(k). a(2k) = 0 for k >= 1, a(3k) = 0 for k >= 1. a(n) = A166586(n) * A166589(n).
%K A167356 nonn,new
%O A167356 1,5
%A A167356 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167355
%S A167355 1,0,5,0,21,0,45,0,25,0,117,0,165,0,105,0,285,0,357,0,225,0,525,0,441,0,
%T A167355 125,0,837,0,957,0,585,0,945,0,1365,0,825,0,1677,0,1845,0,525,0,2205,0,
%U A167355 2025,0
%N A167355 Totally multiplicative sequence with a(p) = (p-2)*(p+2) = p^2-4 for prime p.
%F A167355 Multiplicative with a(p^e) = ((p-2)*(p+2))^e. If n = Product p(k)^e(k) then a(n) = Product ((p(k)-2)*(p(k)+2))^e(k). a(2k) = 0 for k >= 1, a(n) = A166586(n) * A166590(n).
%K A167355 nonn,new
%O A167355 1,3
%A A167355 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167354
%S A167354 1,0,1,0,9,0,25,0,1,0,81,0,121,0,9,0,225,0,289,0,25,0,441,0,81,0,1,0,
%T A167354 729,0,841,0,81,0,225,0,1225,0,121,0,1521,0,1681,0,9,0,2025,0,625,0
%N A167354 Totally multiplicative sequence with a(p) = (p-2)^2 = p^2-4p+4 for prime p.
%F A167354 Multiplicative with a(p^e) = ((p-2)^2)^e. If n = Product p(k)^e(k) then a(n) = Product ((p(k)-2)^2)^e(k). a(2k) = 0 for k >= 1, a(n) = A166586(n)^2.
%K A167354 nonn,new
%O A167354 1,5
%A A167354 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167353
%S A167353 1,15,24,225,48,360,80,3375,576,720,168,5400,224,1200,1152,50625,360,
%T A167353 8640,440,10800,1920,2520,624,81000,2304,3360,13824,18000,960,17280,
%U A167353 1088,759375,4032,5400,3840,129600,1520,6600,5376,162000,1848,28800
%N A167353 Totally multiplicative sequence with a(p) = (p+1)*(p+3) = p^2+4p+3 for prime p.
%F A167353 Multiplicative with a(p^e) = ((p+1)*(p+3))^e. If n = Product p(k)^e(k) then a(n) = Product ((p(k)+1)*(p(k)+3))^e(k). a(n) = A003959(n) * A166591(n).
%K A167353 nonn,new
%O A167353 1,2
%A A167353 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167352
%S A167352 1,3,0,9,12,0,32,27,0,36,96,0,140,96,0,81,252,0,320,108,0,288,480,
%T A167352 0,144,420,0,288,780,0,896,243,0,756,384,0,1292,960,0,324,1596,0,
%U A167352 1760,864,0,1440,2112,0,1024,432
%V A167352 1,-3,0,9,12,0,32,-27,0,-36,96,0,140,-96,0,81,252,0,320,108,0,-288,480,
%W A167352 0,144,-420,0,288,780,0,896,-243,0,-756,384,0,1292,-960,0,-324,1596,0,
%X A167352 1760,864,0,-1440,2112,0,1024,-432
%N A167352 Totally multiplicative sequence with a(p) = (p+1)*(p-3) = p^2-2p-3 for prime p.
%F A167352 Multiplicative with a(p^e) = ((p+1)*(p-3))^e. If n = Product p(k)^e(k) then a(n) = Product ((p(k)+1)*(p(k)-3))^e(k). a(3k) = 0 for k >= 1, a(n) = A003959(n) * A166589(n).
%K A167352 nonn,new
%O A167352 1,2
%A A167352 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167351
%S A167351 1,12,20,144,42,240,72,1728,400,504,156,2880,210,864,840,20736,342,4800,
%T A167351 420,6048,1440,1872,600,34560,1764,2520,8000,10368,930,10080,1056,
%U A167351 248832,3120,4104,3024,57600,1482,5040,4200,72576,1806,17280,1980,22464
%N A167351 Totally multiplicative sequence with a(p) = (p+1)*(p+2) = p^2+3p+2 for prime p.
%F A167351 Multiplicative with a(p^e) = ((p+1)*(p+2))^e. If n = Product p(k)^e(k) then a(n) = Product ((p(k)+1)*(p(k)+2))^e(k). a(n) = A003959(n) * A166590(n).
%K A167351 nonn,new
%O A167351 1,2
%A A167351 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167350
%S A167350 1,0,4,0,18,0,40,0,16,0,108,0,154,0,72,0,270,0,340,0,160,0,504,0,324,0,
%T A167350 64,0,810,0,928,0,432,0,720,0,1330,0,616,0,1638,0,1804,0,288,0,2160,0,
%U A167350 1600,0
%N A167350 Totally multiplicative sequence with a(p) = (p+1)*(p-2) = p^2-p-2 for prime p.
%F A167350 Multiplicative with a(p^e) = ((p+1)*(p-2))^e. If n = Product p(k)^e(k) then a(n) = Product ((p(k)+1)*(p(k)-2))^e(k). a(2k) = 0 for k >= 1, a(n) = A003959(n) * A166586(n).
%K A167350 nonn,new
%O A167350 1,3
%A A167350 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167349
%S A167349 1,9,16,81,36,144,64,729,256,324,144,1296,196,576,576,6561,324,2304,400,
%T A167349 2916,1024,1296,576,11664,1296,1764,4096,5184,900,5184,1024,59049,2304,
%U A167349 2916,2304,20736,1444,3600,3136,26244,1764,9216,1936,11664,9216,5184
%N A167349 Totally multiplicative sequence with a(p) = (p+1)^2 = p^2+2p+1 for prime p.
%F A167349 Multiplicative with a(p^e) = ((p+1)^2)^e. If n = Product p(k)^e(k) then a(n) = Product ((p(k)+1)^2)^e(k). a(n) = A003959(n)^2.
%K A167349 nonn,new
%O A167349 1,2
%A A167349 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A109624
%S A109624 1,5,12,25,32,60,60,125,144,160,140,300,192,300,384,625,320,720,396,800,
%T A109624 720,700,572,1500,1024,960,1728,1500,896,1920,1020,3125,1680,1600,1920,
%U A109624 3600,1440,1980,2304,4000,1760,3600,1932,3500,4608,2860,2300,7500,3600
%N A109624 Totally multiplicative sequence with a(p) = (p-1)*(p+3) = p^2+2p-3 for prime p.
%F A109624 Multiplicative with a(p^e) = ((p-1)*(p+3))^e. If n = Product p(k)^e(k) then a(n) = Product ((p(k)-1)*(p(k)+3))^e(k). a(n) = A003958(n) * A166591(n).
%K A109624 nonn,new
%O A109624 1,2
%A A109624 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167347
%S A167347 1,1,0,1,8,0,24,1,0,8,80,0,120,24,0,1,224,0,288,8,0,80,440,0,64,
%T A167347 120,0,24,728,0,840,1,0,224,192,0,1224,288,0,8,1520,0,1680,80,0,
%U A167347 440,2024,0,576,64
%V A167347 1,-1,0,1,8,0,24,-1,0,-8,80,0,120,-24,0,1,224,0,288,8,0,-80,440,0,64,
%W A167347 -120,0,24,728,0,840,-1,0,-224,192,0,1224,-288,0,-8,1520,0,1680,80,0,
%X A167347 -440,2024,0,576,-64
%N A167347 Totally multiplicative sequence with a(p) = (p-1)*(p-3) = p^2-4p+3 for prime p.
%F A167347 Multiplicative with a(p^e) = ((p-1)*(p-3))^e. If n = Product p(k)^e(k) then a(n) = Product ((p(k)-1)*(p(k)-3))^e(k). a(3k) = 0 for k >= 1, a(n) = A003958(n) * A166589(n).
%K A167347 nonn,new
%O A167347 1,5
%A A167347 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167346
%S A167346 1,4,10,16,28,40,54,64,100,112,130,160,180,216,280,256,304,400,378,448,
%T A167346 540,520,550,640,784,720,1000,864,868,1120,990,1024,1300,1216,1512,1600,
%U A167346 1404,1512,1800,1792,1720,2160,1890,2080,2800,2200,2254,2560,2916,3136
%N A167346 Totally multiplicative sequence with a(p) = (p-1)*(p+2) = p^2+p-2 for prime p.
%F A167346 Multiplicative with a(p^e) = ((p-1)*(p+2))^e. If n = Product p(k)^e(k) then a(n) = Product ((p(k)-1)*(p(k)+2))^e(k). a(n) = A003958(n) * A166590(n).
%K A167346 nonn,new
%O A167346 1,2
%A A167346 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167345
%S A167345 1,0,2,0,12,0,30,0,4,0,90,0,132,0,24,0,240,0,306,0,60,0,462,0,144,0,8,0,
%T A167345 756,0,870,0,180,0,360,0,1260,0,264,0,1560,0,1722,0,48,0,2070,0,900,0
%N A167345 Totally multiplicative sequence with a(p) = (p-1)*(p-2) = p^2-3p+2 for prime p.
%F A167345 Multiplicative with a(p^e) = ((p-1)*(p-2))^e. If n = Product p(k)^e(k) then a(n) = Product ((p(k)-1)*(p(k)-2))^e(k). a(2k) = 0 for k >= 1, a(n) = A003958(n) * A166586(n).
%K A167345 nonn,new
%O A167345 1,3
%A A167345 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167344
%S A167344 1,3,8,9,24,24,48,27,64,72,120,72,168,144,192,81,288,192,360,216,384,
%T A167344 360,528,216,576,504,512,432,840,576,960,243,960,864,1152,576,1368,1080,
%U A167344 1344,648,1680,1152,1848,1080,1536,1584,2208,648,2304,1728
%N A167344 Totally multiplicative sequence with a(p) = (p-1)*(p+1) = p^2-1 for prime p.
%F A167344 Multiplicative with a(p^e) = ((p-1)*(p+1))^e. If n = Product p(k)^e(k) then a(n) = Product ((p(k)-1)*(p(k)+1))^e(k). a(n) = A003958(n) * A003959(n).
%K A167344 nonn,new
%O A167344 1,2
%A A167344 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167343
%S A167343 1,1,4,1,16,4,36,1,16,16,100,4,144,36,64,1,256,16,324,16,144,100,484,4,
%T A167343 256,144,64,36,784,64,900,1,400,256,576,16,1296,324,576,16,1600,144,
%U A167343 1764,100,256,484,2116,4,1296,256
%N A167343 Totally multiplicative sequence with a(p) = (p-1)^2 = p^2-2p+1 for prime p.
%F A167343 Multiplicative with a(p^e) = ((p-1)^2)^e. If n = Product p(k)^e(k) then a(n) = Product ((p(k)-1)^2)^e(k). a(n) = A003958(n)^2.
%K A167343 nonn,new
%O A167343 1,3
%A A167343 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167342
%S A167342 1,10,18,100,40,180,70,1000,324,400,154,1800,208,700,720,10000,340,3240,
%T A167342 418,4000,1260,1540,598,18000,1600,2080,5832,7000,928,7200,1054,100000,
%U A167342 2772,3400,2800,32400,1480,4180,3744,40000,1804,12600,1978,15400,12960
%N A167342 Totally multiplicative sequence with a(p) = p*(p+3) = p^2+3p for prime p.
%F A167342 Multiplicative with a(p^e) = (p*(p+3))^e. If n = Product p(k)^e(k) then a(n) = Product (p(k)*(p(k)+3))^e(k). a(n) = A000027(n) * A166591(n).
%K A167342 nonn,new
%O A167342 1,2
%A A167342 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167341
%S A167341 1,2,0,4,10,0,28,8,0,20,88,0,130,56,0,16,238,0,304,40,0,176,460,0,
%T A167341 100,260,0,112,754,0,868,32,0,476,280,0,1258,608,0,80,1558,0,1720,
%U A167341 352,0,920,2068,0,784,200
%V A167341 1,-2,0,4,10,0,28,-8,0,-20,88,0,130,-56,0,16,238,0,304,40,0,-176,460,0,
%W A167341 100,-260,0,112,754,0,868,-32,0,-476,280,0,1258,-608,0,-80,1558,0,1720,
%X A167341 352,0,-920,2068,0,784,-200
%N A167341 Totally multiplicative sequence with a(p) = p*(p-3) = p^2-3p for prime p.
%F A167341 Multiplicative with a(p^e) = (p*(p-3))^e. If n = Product p(k)^e(k) then a(n) = Product (p(k)*(p(k)-3))^e(k). a(3k) = 0 for k >= 1, a(n) = A000027(n) * A166589(n).
%K A167341 nonn,new
%O A167341 1,2
%A A167341 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167340
%S A167340 1,8,15,64,35,120,63,512,225,280,143,960,195,504,525,4096,323,1800,399,
%T A167340 2240,945,1144,575,7680,1225,1560,3375,4032,899,4200,1023,32768,2145,
%U A167340 2584,2205,14400,1443,3192,2925,17920,1763,7560,1935,9152,7875,4600
%N A167340 Totally multiplicative sequence with a(p) = p*(p+2) = p^2+2p for prime p.
%F A167340 Multiplicative with a(p^e) = (p*(p+2))^e. If n = Product p(k)^e(k) then a(n) = Product (p(k)*(p(k)+2))^e(k). a(n) = A000027(n) * A166590(n).
%K A167340 nonn,new
%O A167340 1,2
%A A167340 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167339
%S A167339 1,0,3,0,15,0,35,0,9,0,99,0,143,0,45,0,255,0,323,0,105,0,483,0,225,0,27,
%T A167339 0,783,0,899,0,297,0,525,0,1295,0,429,0,1599,0,1763,0,135,0,2115,0,1225,
%U A167339 0
%N A167339 Totally multiplicative sequence with a(p) = p*(p-2) = p^2-2p for prime p.
%F A167339 Multiplicative with a(p^e) = (p*(p-2))^e. If n = Product p(k)^e(k) then a(n) = Product (p(k)*(p(k)-2))^e(k). a(2k) = 0 for k >= 1, a(n) = A000027(n) * A166586(n).
%K A167339 nonn,new
%O A167339 1,3
%A A167339 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167338
%S A167338 1,6,12,36,30,72,56,216,144,180,132,432,182,336,360,1296,306,864,380,
%T A167338 1080,672,792,552,2592,900,1092,1728,2016,870,2160,992,7776,1584,1836,
%U A167338 1680,5184,1406,2280,2184,6480,1722,4032,1892,4752,4320,3312,2256,15552
%N A167338 Totally multiplicative sequence with a(p) = p*(p+1) = p^2+p for prime p.
%F A167338 Multiplicative with a(p^e) = (p*(p+1))^e. If n = Product p(k)^e(k) then a(n) = Product (p(k)*(p(k)+1))^e(k). a(n) = A000027(n) * A003959(n).
%K A167338 nonn,new
%O A167338 1,2
%A A167338 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167337
%S A167337 1,22,32,484,52,704,72,10648,1024,1144,112,15488,132,1584,1664,234256,
%T A167337 172,22528,192,25168,2304,2464,232,340736,2704,2904,32768,34848,292,
%U A167337 36608,312,5153632,3584,3784,3744,495616,372,4224,4224,553696,412,50688
%N A167337 Totally multiplicative sequence with a(p) = 2*(5p+1) = 10p+2 for prime p.
%F A167337 Multiplicative with a(p^e) = (2*(5p+1))^e. If n = Product p(k)^e(k) then a(n) = Product (2*(5*p(k)+1))^e(k). a(n) = A061142(n) * A166663(n) = 2^bigomega(n) * A166663(n) = 2^A001222(n) * A166663(n).
%K A167337 nonn,new
%O A167337 1,2
%A A167337 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167336
%S A167336 1,18,26,324,42,468,58,5832,676,756,90,8424,106,1044,1092,104976,138,
%T A167336 12168,154,13608,1508,1620,186,151632,1764,1908,17576,18792,234,19656,
%U A167336 250,1889568,2340,2484,2436,219024,298,2772,2756,244944,330,27144,346
%N A167336 Totally multiplicative sequence with a(p) = 2*(4p+1) = 8p+2 for prime p.
%F A167336 Multiplicative with a(p^e) = (2*(4p+1))^e. If n = Product p(k)^e(k) then a(n) = Product (2*(4*p(k)+1))^e(k). a(n) = A061142(n) * A166662(n) = 2^bigomega(n) * A166662(n) = 2^A001222(n) * A166662(n).
%K A167336 nonn,new
%O A167336 1,2
%A A167336 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167335
%S A167335 1,14,20,196,32,280,44,2744,400,448,68,3920,80,616,640,38416,104,5600,
%T A167335 116,6272,880,952,140,54880,1024,1120,8000,8624,176,8960,188,537824,
%U A167335 1360,1456,1408,78400,224,1624,1600,87808,248,12320,260,13328,12800
%N A167335 Totally multiplicative sequence with a(p) = 2*(3p+1) = 6p+2 for prime p.
%F A167335 Multiplicative with a(p^e) = (2*(3p+1))^e. If n = Product p(k)^e(k) then a(n) = Product (2*(3*p(k)+1))^e(k). a(n) = A061142(n) * A166661(n) = 2^bigomega(n) * A166661(n) = 2^A001222(n) * A166661(n).
%K A167335 nonn,new
%O A167335 1,2
%A A167335 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167334
%S A167334 1,10,14,100,22,140,30,1000,196,220,46,1400,54,300,308,10000,70,1960,78,
%T A167334 2200,420,460,94,14000,484,540,2744,3000,118,3080,126,100000,644,700,
%U A167334 660,19600,150,780,756,22000,166,4200,174,4600,4312,940,190,140000,900
%N A167334 Totally multiplicative sequence with a(p) = 2*(2p+1) = 4p+2 for prime p.
%F A167334 Multiplicative with a(p^e) = (2*(2p+1))^e. If n = Product p(k)^e(k) then a(n) = Product (2*(2*p(k)+1))^e(k). a(n) = A061142(n) * A166660(n) = 2^bigomega(n) * A166660(n) = 2^A001222(n) * A166660(n).
%K A167334 nonn,new
%O A167334 1,2
%A A167334 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167333
%S A167333 1,18,28,324,48,504,68,5832,784,864,108,9072,128,1224,1344,104976,168,
%T A167333 14112,188,15552,1904,1944,228,163296,2304,2304,21952,22032,288,24192,
%U A167333 308,1889568,3024,3024,3264,254016,368,3384,3584,279936,408,34272,428
%N A167333 Totally multiplicative sequence with a(p) = 2*(5p-1) = 10p-2 for prime p.
%F A167333 Multiplicative with a(p^e) = (2*(5p-1))^e. If n = Product p(k)^e(k) then a(n) = Product (2*(5*p(k)-1))^e(k). a(n) = A061142(n) * A166654(n) = 2^bigomega(n) * A166654(n) = 2^A001222(n) * A166654(n).
%K A167333 nonn,new
%O A167333 1,2
%A A167333 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167332
%S A167332 1,14,22,196,38,308,54,2744,484,532,86,4312,102,756,836,38416,134,6776,
%T A167332 150,7448,1188,1204,182,60368,1444,1428,10648,10584,230,11704,246,
%U A167332 537824,1892,1876,2052,94864,294,2100,2244,104272,326,16632,342,16856
%N A167332 Totally multiplicative sequence with a(p) = 2*(4p-1) = 8p-2 for prime p.
%F A167332 Multiplicative with a(p^e) = (2*(4p-1))^e. If n = Product p(k)^e(k) then a(n) = Product (2*(4*p(k)-1))^e(k). a(n) = A061142(n) * A166653(n) = 2^bigomega(n) * A166653(n) = 2^A001222(n) * A166653(n).
%K A167332 nonn,new
%O A167332 1,2
%A A167332 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167331
%S A167331 1,10,16,100,28,160,40,1000,256,280,64,1600,76,400,448,10000,100,2560,
%T A167331 112,2800,640,640,136,16000,784,760,4096,4000,172,4480,184,100000,1024,
%U A167331 1000,1120,25600,220,1120,1216,28000,244,6400,256,6400,7168,1360,280
%N A167331 Totally multiplicative sequence with a(p) = 2*(3p-1) = 6p-2 for prime p.
%F A167331 Multiplicative with a(p^e) = (2*(3p-1))^e. If n = Product p(k)^e(k) then a(n) = Product (2*(3*p(k)-1))^e(k). a(n) = A061142(n) * A166652(n) = 2^bigomega(n) * A166652(n) = 2^A001222(n) * A166652(n).
%K A167331 nonn,new
%O A167331 1,2
%A A167331 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167330
%S A167330 1,6,10,36,18,60,26,216,100,108,42,360,50,156,180,1296,66,600,74,648,
%T A167330 260,252,90,2160,324,300,1000,936,114,1080,122,7776,420,396,468,3600,
%U A167330 146,444,500,3888,162,1560,170,1512,1800,540,186,12960,676,1944
%N A167330 Totally multiplicative sequence with a(p) = 2*(2p-1) = 4p-2 for prime p.
%F A167330 Multiplicative with a(p^e) = (2*(2p-1))^e. If n = Product p(k)^e(k) then a(n) = Product (2*(2*p(k)-1))^e(k). a(n) = A061142(n) * A166651(n) = 2^bigomega(n) * A166651(n) = 2^A001222(n) * A166651(n).
%K A167330 nonn,new
%O A167330 1,2
%A A167330 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167329
%S A167329 1,50,60,2500,80,3000,100,125000,3600,4000,140,150000,160,5000,4800,
%T A167329 6250000,200,180000,220,200000,6000,7000,260,7500000,6400,8000,216000,
%U A167329 250000,320,240000,340,312500000,8400,10000,8000,9000000,400,11000,9600
%N A167329 Totally multiplicative sequence with a(p) = 10*(p+3) for prime p.
%F A167329 Multiplicative with a(p^e) = (10*(p+3))^e. If n = Product p(k)^e(k) then a(n) = Product (10*(p(k)+3))^e(k). a(n) = A165831(n) * A166591(n) = 10^bigomega(n) * A166591(n) = 10^A001222(n) * A166591(n).
%K A167329 nonn,new
%O A167329 1,2
%A A167329 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167328
%S A167328 1,45,54,2025,72,2430,90,91125,2916,3240,126,109350,144,4050,3888,
%T A167328 4100625,180,131220,198,145800,4860,5670,234,4920750,5184,6480,157464,
%U A167328 182250,288,174960,306,184528125,6804,8100,6480,5904900,360,8910,7776
%N A167328 Totally multiplicative sequence with a(p) = 9*(p+3) for prime p.
%F A167328 Multiplicative with a(p^e) = (9*(p+3))^e. If n = Product p(k)^e(k) then a(n) = Product (9*(p(k)+3))^e(k). a(n) = A165830(n) * A166591(n) = 9^bigomega(n) * A166591(n) = 9^A001222(n) * A166591(n).
%K A167328 nonn,new
%O A167328 1,2
%A A167328 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167327
%S A167327 1,40,48,1600,64,1920,80,64000,2304,2560,112,76800,128,3200,3072,
%T A167327 2560000,160,92160,176,102400,3840,4480,208,3072000,4096,5120,110592,
%U A167327 128000,256,122880,272,102400000,5376,6400,5120,3686400,320,7040,6144
%N A167327 Totally multiplicative sequence with a(p) = 8*(p+3) for prime p.
%F A167327 Multiplicative with a(p^e) = (8*(p+3))^e. If n = Product p(k)^e(k) then a(n) = Product (8*(p(k)+3))^e(k). a(n) = A165829(n) * A166591(n) = 8^bigomega(n) * A166591(n) = 8^A001222(n) * A166591(n).
%K A167327 nonn,new
%O A167327 1,2
%A A167327 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167326
%S A167326 1,35,42,1225,56,1470,70,42875,1764,1960,98,51450,112,2450,2352,1500625,
%T A167326 140,61740,154,68600,2940,3430,182,1800750,3136,3920,74088,85750,224,
%U A167326 82320,238,52521875,4116,4900,3920,2160900,280,5390,4704,2401000,308
%N A167326 Totally multiplicative sequence with a(p) = 7*(p+3) for prime p.
%F A167326 Multiplicative with a(p^e) = (7*(p+3))^e. If n = Product p(k)^e(k) then a(n) = Product (7*(p(k)+3))^e(k). a(n) = A165828(n) * A166591(n) = 7^bigomega(n) * A166591(n) = 7^A001222(n) * A166591(n).
%K A167326 nonn,new
%O A167326 1,2
%A A167326 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167325
%S A167325 1,30,36,900,48,1080,60,27000,1296,1440,84,32400,96,1800,1728,810000,
%T A167325 120,38880,132,43200,2160,2520,156,972000,2304,2880,46656,54000,192,
%U A167325 51840,204,24300000,3024,3600,2880,1166400,240,3960,3456,1296000,264
%N A167325 Totally multiplicative sequence with a(p) = 6*(p+3) for prime p.
%F A167325 Multiplicative with a(p^e) = (6*(p+3))^e. If n = Product p(k)^e(k) then a(n) = Product (6*(p(k)+3))^e(k). a(n) = A165827(n) * A166591(n) = 6^bigomega(n) * A166591(n) = 6^A001222(n) * A166591(n).
%K A167325 nonn,new
%O A167325 1,2
%A A167325 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167324
%S A167324 1,25,30,625,40,750,50,15625,900,1000,70,18750,80,1250,1200,390625,100,
%T A167324 22500,110,25000,1500,1750,130,468750,1600,2000,27000,31250,160,30000,
%U A167324 170,9765625,2100,2500,2000,562500,200,2750,2400,625000,220,37500,230
%N A167324 Totally multiplicative sequence with a(p) = 5*(p+3) for prime p.
%F A167324 Multiplicative with a(p^e) = (5*(p+3))^e. If n = Product p(k)^e(k) then a(n) = Product (5*(p(k)+3))^e(k). a(n) = A165826(n) * A166591(n) = 5^bigomega(n) * A166591(n) = 5^A001222(n) * A166591(n).
%K A167324 nonn,new
%O A167324 1,2
%A A167324 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167323
%S A167323 1,20,24,400,32,480,40,8000,576,640,56,9600,64,800,768,160000,80,11520,
%T A167323 88,12800,960,1120,104,192000,1024,1280,13824,16000,128,15360,136,
%U A167323 3200000,1344,1600,1280,230400,160,1760,1536,256000,176,19200,184,22400
%N A167323 Totally multiplicative sequence with a(p) = 4*(p+3) for prime p.
%F A167323 Multiplicative with a(p^e) = (4*(p+3))^e. If n = Product p(k)^e(k) then a(n) = Product (4*(p(k)+3))^e(k). a(n) = A165825(n) * A166591(n) = 4^bigomega(n) * A166591(n) = 4^A001222(n) * A166591(n).
%K A167323 nonn,new
%O A167323 1,2
%A A167323 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167322
%S A167322 1,15,18,225,24,270,30,3375,324,360,42,4050,48,450,432,50625,60,4860,66,
%T A167322 5400,540,630,78,60750,576,720,5832,6750,96,6480,102,759375,756,900,720,
%U A167322 72900,120,990,864,81000,132,8100,138,9450,7776,1170,150,911250,900
%N A167322 Totally multiplicative sequence with a(p) = 3*(p+3) for prime p.
%F A167322 Multiplicative with a(p^e) = (3*(p+3))^e. If n = Product p(k)^e(k) then a(n) = Product (3*(p(k)+3))^e(k). a(n) = A165824(n) * A166591(n) = 3^bigomega(n) * A166591(n) = 3^A001222(n) * A166591(n).
%K A167322 nonn,new
%O A167322 1,2
%A A167322 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167321
%S A167321 1,10,12,100,16,120,20,1000,144,160,28,1200,32,200,192,10000,40,1440,44,
%T A167321 1600,240,280,52,12000,256,320,1728,2000,64,1920,68,100000,336,400,320,
%U A167321 14400,80,440,384,16000,88,2400,92,2800,2304,520,100,120000,400,2560
%N A167321 Totally multiplicative sequence with a(p) = 2*(p+3) for prime p.
%F A167321 Multiplicative with a(p^e) = (2*(p+3))^e. If n = Product p(k)^e(k) then a(n) = Product (2*(p(k)+3))^e(k). a(n) = A061142(n) * A166591(n) = 2^bigomega(n) * A166591(n) = 2^A001222(n) * A166591(n).
%K A167321 nonn,new
%O A167321 1,2
%A A167321 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167320
%S A167320 1,10,0,100,20,0,40,1000,0,200,80,0,100,400,0,10000,140,0,160,2000,
%T A167320 0,800,200,0,400,1000,0,4000,260,0,280,100000,0,1400,800,0,340,
%U A167320 1600,0,20000,380,0,400,8000,0,2000,440,0,1600,4000
%V A167320 1,-10,0,100,20,0,40,-1000,0,-200,80,0,100,-400,0,10000,140,0,160,2000,
%W A167320 0,-800,200,0,400,-1000,0,4000,260,0,280,-100000,0,-1400,800,0,340,
%X A167320 -1600,0,-20000,380,0,400,8000,0,-2000,440,0,1600,-4000
%N A167320 Totally multiplicative sequence with a(p) = 10*(p-3) for prime p.
%F A167320 Multiplicative with a(p^e) = (10*(p-3))^e. If n = Product p(k)^e(k) then a(n) = Product (10*(p(k)-3))^e(k). a(3k) = 0 for k >= 1. a(n) = A165831(n) * A166589(n) = 10^bigomega(n) * A166589(n) = 10^A001222(n) * A166589(n).
%K A167320 nonn,new
%O A167320 1,2
%A A167320 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167319
%S A167319 1,9,0,81,18,0,36,729,0,162,72,0,90,324,0,6561,126,0,144,1458,0,
%T A167319 648,180,0,324,810,0,2916,234,0,252,59049,0,1134,648,0,306,1296,0,
%U A167319 13122,342,0,360,5832,0,1620,396,0,1296,2916
%V A167319 1,-9,0,81,18,0,36,-729,0,-162,72,0,90,-324,0,6561,126,0,144,1458,0,
%W A167319 -648,180,0,324,-810,0,2916,234,0,252,-59049,0,-1134,648,0,306,-1296,0,
%X A167319 -13122,342,0,360,5832,0,-1620,396,0,1296,-2916
%N A167319 Totally multiplicative sequence with a(p) = 9*(p-3) for prime p.
%F A167319 Multiplicative with a(p^e) = (9*(p-3))^e. If n = Product p(k)^e(k) then a(n) = Product (9*(p(k)-3))^e(k). a(3k) = 0 for k >= 1. a(n) = A165830(n) * A166589(n) = 9^bigomega(n) * A166589(n) = 9^A001222(n) * A166589(n).
%K A167319 nonn,new
%O A167319 1,2
%A A167319 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167318
%S A167318 1,8,0,64,16,0,32,512,0,128,64,0,80,256,0,4096,112,0,128,1024,0,
%T A167318 512,160,0,256,640,0,2048,208,0,224,32768,0,896,512,0,272,1024,0,
%U A167318 8192,304,0,320,4096,0,1280,352,0,1024,2048
%V A167318 1,-8,0,64,16,0,32,-512,0,-128,64,0,80,-256,0,4096,112,0,128,1024,0,
%W A167318 -512,160,0,256,-640,0,2048,208,0,224,-32768,0,-896,512,0,272,-1024,0,
%X A167318 -8192,304,0,320,4096,0,-1280,352,0,1024,-2048
%N A167318 Totally multiplicative sequence with a(p) = 8*(p-3) for prime p.
%F A167318 Multiplicative with a(p^e) = (8*(p-3))^e. If n = Product p(k)^e(k) then a(n) = Product (8*(p(k)-3))^e(k). a(3k) = 0 for k >= 1. a(n) = A165829(n) * A166589(n) = 8^bigomega(n) * A166589(n) = 8^A001222(n) * A166589(n).
%K A167318 nonn,new
%O A167318 1,2
%A A167318 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167317
%S A167317 1,7,0,49,14,0,28,343,0,98,56,0,70,196,0,2401,98,0,112,686,0,392,
%T A167317 140,0,196,490,0,1372,182,0,196,16807,0,686,392,0,238,784,0,4802,
%U A167317 266,0,280,2744,0,980,308,0,784,1372
%V A167317 1,-7,0,49,14,0,28,-343,0,-98,56,0,70,-196,0,2401,98,0,112,686,0,-392,
%W A167317 140,0,196,-490,0,1372,182,0,196,-16807,0,-686,392,0,238,-784,0,-4802,
%X A167317 266,0,280,2744,0,-980,308,0,784,-1372
%N A167317 Totally multiplicative sequence with a(p) = 7*(p-3) for prime p.
%F A167317 Multiplicative with a(p^e) = (7*(p-3))^e. If n = Product p(k)^e(k) then a(n) = Product (7*(p(k)-3))^e(k). a(3k) = 0 for k >= 1. a(n) = A165828(n) * A166589(n) = 7^bigomega(n) * A166589(n) = 7^A001222(n) * A166589(n).
%K A167317 nonn,new
%O A167317 1,2
%A A167317 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167316
%S A167316 1,6,0,36,12,0,24,216,0,72,48,0,60,144,0,1296,84,0,96,432,0,288,
%T A167316 120,0,144,360,0,864,156,0,168,7776,0,504,288,0,204,576,0,2592,228,
%U A167316 0,240,1728,0,720,264,0,576,864
%V A167316 1,-6,0,36,12,0,24,-216,0,-72,48,0,60,-144,0,1296,84,0,96,432,0,-288,
%W A167316 120,0,144,-360,0,864,156,0,168,-7776,0,-504,288,0,204,-576,0,-2592,228,
%X A167316 0,240,1728,0,-720,264,0,576,-864
%N A167316 Totally multiplicative sequence with a(p) = 6*(p-3) for prime p.
%F A167316 Multiplicative with a(p^e) = (6*(p-3))^e. If n = Product p(k)^e(k) then a(n) = Product (6*(p(k)-3))^e(k). a(3k) = 0 for k >= 1. a(n) = A165827(n) * A166589(n) = 6^bigomega(n) * A166589(n) = 6^A001222(n) * A166589(n).
%K A167316 nonn,new
%O A167316 1,2
%A A167316 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167315
%S A167315 1,5,0,25,10,0,20,125,0,50,40,0,50,100,0,625,70,0,80,250,0,200,100,
%T A167315 0,100,250,0,500,130,0,140,3125,0,350,200,0,170,400,0,1250,190,0,
%U A167315 200,1000,0,500,220,0,400,500
%V A167315 1,-5,0,25,10,0,20,-125,0,-50,40,0,50,-100,0,625,70,0,80,250,0,-200,100,
%W A167315 0,100,-250,0,500,130,0,140,-3125,0,-350,200,0,170,-400,0,-1250,190,0,
%X A167315 200,1000,0,-500,220,0,400,-500
%N A167315 Totally multiplicative sequence with a(p) = 5*(p-3) for prime p.
%F A167315 Multiplicative with a(p^e) = (5*(p-3))^e. If n = Product p(k)^e(k) then a(n) = Product (5*(p(k)-3))^e(k). a(3k) = 0 for k >= 1. a(n) = A165826(n) * A166589(n) = 5^bigomega(n) * A166589(n) = 5^A001222(n) * A166589(n).
%K A167315 nonn,new
%O A167315 1,2
%A A167315 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167314
%S A167314 1,4,0,16,8,0,16,64,0,32,32,0,40,64,0,256,56,0,64,128,0,128,80,0,
%T A167314 64,160,0,256,104,0,112,1024,0,224,128,0,136,256,0,512,152,0,160,
%U A167314 512,0,320,176,0,256,256
%V A167314 1,-4,0,16,8,0,16,-64,0,-32,32,0,40,-64,0,256,56,0,64,128,0,-128,80,0,
%W A167314 64,-160,0,256,104,0,112,-1024,0,-224,128,0,136,-256,0,-512,152,0,160,
%X A167314 512,0,-320,176,0,256,-256
%N A167314 Totally multiplicative sequence with a(p) = 4*(p-3) for prime p.
%F A167314 Multiplicative with a(p^e) = (4*(p-3))^e. If n = Product p(k)^e(k) then a(n) = Product (4*(p(k)-3))^e(k). a(3k) = 0 for k >= 1. a(n) = A165825(n) * A166589(n) = 4^bigomega(n) * A166589(n) = 4^A001222(n) * A166589(n).
%K A167314 nonn,new
%O A167314 1,2
%A A167314 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167313
%S A167313 1,3,0,9,6,0,12,27,0,18,24,0,30,36,0,81,42,0,48,54,0,72,60,0,36,
%T A167313 90,0,108,78,0,84,243,0,126,72,0,102,144,0,162,114,0,120,216,0,
%U A167313 180,132,0,144,108
%V A167313 1,-3,0,9,6,0,12,-27,0,-18,24,0,30,-36,0,81,42,0,48,54,0,-72,60,0,36,
%W A167313 -90,0,108,78,0,84,-243,0,-126,72,0,102,-144,0,-162,114,0,120,216,0,
%X A167313 -180,132,0,144,-108
%N A167313 Totally multiplicative sequence with a(p) = 3*(p-3) for prime p.
%F A167313 Multiplicative with a(p^e) = (3*(p-3))^e. If n = Product p(k)^e(k) then a(n) = Product (3*(p(k)-3))^e(k). a(3k) = 0 for k >= 1. a(n) = A165824(n) * A166589(n) = 3^bigomega(n) * A166589(n) = 3^A001222(n) * A166589(n).
%K A167313 nonn,new
%O A167313 1,2
%A A167313 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167312
%S A167312 1,2,0,4,4,0,8,8,0,8,16,0,20,16,0,16,28,0,32,16,0,32,40,0,16,40,0,
%T A167312 32,52,0,56,32,0,56,32,0,68,64,0,32,76,0,80,64,0,80,88,0,64,32
%V A167312 1,-2,0,4,4,0,8,-8,0,-8,16,0,20,-16,0,16,28,0,32,16,0,-32,40,0,16,-40,0,
%W A167312 32,52,0,56,-32,0,-56,32,0,68,-64,0,-32,76,0,80,64,0,-80,88,0,64,-32
%N A167312 Totally multiplicative sequence with a(p) = 2*(p-3) for prime p.
%F A167312 Multiplicative with a(p^e) = (2*(p-3))^e. If n = Product p(k)^e(k) then a(n) = Product (2*(p(k)-3))^e(k). a(3k) = 0 for k >= 1. a(n) = A061142(n) * A166589(n) = 2^bigomega(n) * A166589(n) = 2^A001222(n) * A166589(n).
%K A167312 nonn,new
%O A167312 1,2
%A A167312 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167311
%S A167311 1,40,50,1600,70,2000,90,64000,2500,2800,130,80000,150,3600,3500,
%T A167311 2560000,190,100000,210,112000,4500,5200,250,3200000,4900,6000,125000,
%U A167311 144000,310,140000,330,102400000,6500,7600,6300,4000000,390,8400,7500
%N A167311 Totally multiplicative sequence with a(p) = 10*(p+2) for prime p.
%F A167311 Multiplicative with a(p^e) = (10*(p+2))^e. If n = Product p(k)^e(k) then a(n) = Product (10*(p(k)+2))^e(k). a(n) = A165831(n) * A166590(n) = 10^bigomega(n) * A166590(n) = 10^A001222(n) * A166590(n).
%K A167311 nonn,new
%O A167311 1,2
%A A167311 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167310
%S A167310 1,36,45,1296,63,1620,81,46656,2025,2268,117,58320,135,2916,2835,
%T A167310 1679616,171,72900,189,81648,3645,4212,225,2099520,3969,4860,91125,
%U A167310 104976,279,102060,297,60466176,5265,6156,5103,2624400,351,6804,6075
%N A167310 Totally multiplicative sequence with a(p) = 9*(p+2) for prime p.
%F A167310 Multiplicative with a(p^e) = (9*(p+2))^e. If n = Product p(k)^e(k) then a(n) = Product (9*(p(k)+2))^e(k). a(n) = A165830(n) * A166590(n) = 9^bigomega(n) * A166590(n) = 9^A001222(n) * A166590(n).
%K A167310 nonn,new
%O A167310 1,2
%A A167310 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167309
%S A167309 1,32,40,1024,56,1280,72,32768,1600,1792,104,40960,120,2304,2240,
%T A167309 1048576,152,51200,168,57344,2880,3328,200,1310720,3136,3840,64000,
%U A167309 73728,248,71680,264,33554432,4160,4864,4032,1638400,312,5376,4800
%N A167309 Totally multiplicative sequence with a(p) = 8*(p+2) for prime p.
%F A167309 Multiplicative with a(p^e) = (8*(p+2))^e. If n = Product p(k)^e(k) then a(n) = Product (8*(p(k)+2))^e(k). a(n) = A165829(n) * A166590(n) = 8^bigomega(n) * A166590(n) = 8^A001222(n) * A166590(n).
%K A167309 nonn,new
%O A167309 1,2
%A A167309 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167308
%S A167308 1,28,35,784,49,980,63,21952,1225,1372,91,27440,105,1764,1715,614656,
%T A167308 133,34300,147,38416,2205,2548,175,768320,2401,2940,42875,49392,217,
%U A167308 48020,231,17210368,3185,3724,3087,960400,273,4116,3675,1075648,301
%N A167308 Totally multiplicative sequence with a(p) = 7*(p+2) for prime p.
%F A167308 Multiplicative with a(p^e) = (7*(p+2))^e. If n = Product p(k)^e(k) then a(n) = Product (7*(p(k)+2))^e(k). a(n) = A165828(n) * A166590(n) = 7^bigomega(n) * A166590(n) = 7^A001222(n) * A166590(n).
%K A167308 nonn,new
%O A167308 1,2
%A A167308 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167307
%S A167307 1,24,30,576,42,720,54,13824,900,1008,78,17280,90,1296,1260,331776,114,
%T A167307 21600,126,24192,1620,1872,150,414720,1764,2160,27000,31104,186,30240,
%U A167307 198,7962624,2340,2736,2268,518400,234,3024,2700,580608,258,38880,270
%N A167307 Totally multiplicative sequence with a(p) = 6*(p+2) for prime p.
%F A167307 Multiplicative with a(p^e) = (6*(p+2))^e. If n = Product p(k)^e(k) then a(n) = Product (6*(p(k)+2))^e(k). a(n) = A165827(n) * A166590(n) = 6^bigomega(n) * A166590(n) = 6^A001222(n) * A166590(n).
%K A167307 nonn,new
%O A167307 1,2
%A A167307 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167306
%S A167306 1,20,25,400,35,500,45,8000,625,700,65,10000,75,900,875,160000,95,12500,
%T A167306 105,14000,1125,1300,125,200000,1225,1500,15625,18000,155,17500,165,
%U A167306 3200000,1625,1900,1575,250000,195,2100,1875,280000,215,22500,225,26000
%N A167306 Totally multiplicative sequence with a(p) = 5*(p+2) for prime p.
%F A167306 Multiplicative with a(p^e) = (5*(p+2))^e. If n = Product p(k)^e(k) then a(n) = Product (5*(p(k)+2))^e(k). a(n) = A165826(n) * A166590(n) = 5^bigomega(n) * A166590(n) = 5^A001222(n) * A166590(n).
%K A167306 nonn,new
%O A167306 1,2
%A A167306 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167305
%S A167305 1,16,20,256,28,320,36,4096,400,448,52,5120,60,576,560,65536,76,6400,84,
%T A167305 7168,720,832,100,81920,784,960,8000,9216,124,8960,132,1048576,1040,
%U A167305 1216,1008,102400,156,1344,1200,114688,172,11520,180,13312,11200,1600
%N A167305 Totally multiplicative sequence with a(p) = 4*(p+2) for prime p.
%F A167305 Multiplicative with a(p^e) = (4*(p+2))^e. If n = Product p(k)^e(k) then a(n) = Product (4*(p(k)+2))^e(k). a(n) = A165825(n) * A166590(n) = 4^bigomega(n) * A166590(n) = 4^A001222(n) * A166590(n).
%K A167305 nonn,new
%O A167305 1,2
%A A167305 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167304
%S A167304 1,12,15,144,21,180,27,1728,225,252,39,2160,45,324,315,20736,57,2700,63,
%T A167304 3024,405,468,75,25920,441,540,3375,3888,93,3780,99,248832,585,684,567,
%U A167304 32400,117,756,675,36288,129,4860,135,5616,4725,900,147,311040,729,5292
%N A167304 Totally multiplicative sequence with a(p) = 3*(p+2) for prime p.
%F A167304 Multiplicative with a(p^e) = (3*(p+2))^e. If n = Product p(k)^e(k) then a(n) = Product (3*(p(k)+2))^e(k). a(n) = A165824(n) * A166590(n) = 3^bigomega(n) * A166590(n) = 3^A001222(n) * A166590(n).
%K A167304 nonn,new
%O A167304 1,2
%A A167304 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167303
%S A167303 1,8,10,64,14,80,18,512,100,112,26,640,30,144,140,4096,38,800,42,896,
%T A167303 180,208,50,5120,196,240,1000,1152,62,1120,66,32768,260,304,252,6400,78,
%U A167303 336,300,7168,86,1440,90,1664,1400,400,98,40960,324,1568
%N A167303 Totally multiplicative sequence with a(p) = 2*(p+2) for prime p.
%F A167303 Multiplicative with a(p^e) = (2*(p+2))^e. If n = Product p(k)^e(k) then a(n) = Product (2*(p(k)+2))^e(k). a(n) = A061142(n) * A166590(n) = 2^bigomega(n) * A166590(n) = 2^A001222(n) * A166590(n).
%K A167303 nonn,new
%O A167303 1,2
%A A167303 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167302
%S A167302 1,0,10,0,30,0,50,0,100,0,90,0,110,0,300,0,150,0,170,0,500,0,210,0,900,
%T A167302 0,1000,0,270,0,290,0,900,0,1500,0,350,0,1100,0,390,0,410,0,3000,0,450,
%U A167302 0,2500,0
%N A167302 Totally multiplicative sequence with a(p) = 10*(p-2) for prime p.
%F A167302 Multiplicative with a(p^e) = (10*(p-2))^e. If n = Product p(k)^e(k) then a(n) = Product (10*(p(k)-2))^e(k). a(2k) = 0 for k >= 1. a(n) = A165831(n) * A166586(n) = 10^bigomega(n) * A166586(n) = 10^A001222(n) * A166586(n).
%K A167302 nonn,new
%O A167302 1,3
%A A167302 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167301
%S A167301 1,0,9,0,27,0,45,0,81,0,81,0,99,0,243,0,135,0,153,0,405,0,189,0,729,0,
%T A167301 729,0,243,0,261,0,729,0,1215,0,315,0,891,0,351,0,369,0,2187,0,405,0,
%U A167301 2025,0
%N A167301 Totally multiplicative sequence with a(p) = 9*(p-2) for prime p.
%F A167301 Multiplicative with a(p^e) = (9*(p-2))^e. If n = Product p(k)^e(k) then a(n) = Product (9*(p(k)-2))^e(k). a(2k) = 0 for k >= 1. a(n) = A165830(n) * A166586(n) = 9^bigomega(n) * A166586(n) = 9^A001222(n) * A166586(n).
%K A167301 nonn,new
%O A167301 1,3
%A A167301 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167300
%S A167300 1,0,8,0,24,0,40,0,64,0,72,0,88,0,192,0,120,0,136,0,320,0,168,0,576,0,
%T A167300 512,0,216,0,232,0,576,0,960,0,280,0,704,0,312,0,328,0,1536,0,360,0,
%U A167300 1600,0
%N A167300 Totally multiplicative sequence with a(p) = 8*(p-2) for prime p.
%F A167300 Multiplicative with a(p^e) = (8*(p-2))^e. If n = Product p(k)^e(k) then a(n) = Product (8*(p(k)-2))^e(k). a(2k) = 0 for k >= 1. a(n) = A165829(n) * A166586(n) = 8^bigomega(n) * A166586(n) = 8^A001222(n) * A166586(n).
%K A167300 nonn,new
%O A167300 1,3
%A A167300 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167299
%S A167299 1,0,7,0,21,0,35,0,49,0,63,0,77,0,147,0,105,0,119,0,245,0,147,0,441,0,
%T A167299 343,0,189,0,203,0,441,0,735,0,245,0,539,0,273,0,287,0,1029,0,315,0,
%U A167299 1225,0
%N A167299 Totally multiplicative sequence with a(p) = 7*(p-2) for prime p.
%F A167299 Multiplicative with a(p^e) = (7*(p-2))^e. If n = Product p(k)^e(k) then a(n) = Product (7*(p(k)-2))^e(k). a(2k) = 0 for k >= 1. a(n) = A165828(n) * A166586(n) = 7^bigomega(n) * A166586(n) = 7^A001222(n) * A166586(n).
%K A167299 nonn,new
%O A167299 1,3
%A A167299 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167298
%S A167298 1,0,6,0,18,0,30,0,36,0,54,0,66,0,108,0,90,0,102,0,180,0,126,0,324,0,
%T A167298 216,0,162,0,174,0,324,0,540,0,210,0,396,0,234,0,246,0,648,0,270,0,900,
%U A167298 0
%N A167298 Totally multiplicative sequence with a(p) = 6*(p-2) for prime p.
%F A167298 Multiplicative with a(p^e) = (5*(p-2))^e. If n = Product p(k)^e(k) then a(n) = Product (6*(p(k)-2))^e(k). a(2k) = 0 for k >= 1. a(n) = A165827(n) * A166586(n) = 6^bigomega(n) * A166586(n) = 6^A001222(n) * A166586(n).
%K A167298 nonn,new
%O A167298 1,3
%A A167298 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167297
%S A167297 1,0,5,0,15,0,25,0,25,0,45,0,55,0,75,0,75,0,85,0,125,0,105,0,225,0,125,
%T A167297 0,135,0,145,0,225,0,375,0,175,0,275,0,195,0,205,0,375,0,225,0,625,0
%N A167297 Totally multiplicative sequence with a(p) = 5*(p-2) for prime p.
%F A167297 Multiplicative with a(p^e) = (5*(p-2))^e. If n = Product p(k)^e(k) then a(n) = Product (5*(p(k)-2))^e(k). a(2k) = 0 for k >= 1. a(n) = A165826(n) * A166586(n) = 5^bigomega(n) * A166586(n) = 5^A001222(n) * A166586(n).
%K A167297 nonn,new
%O A167297 1,3
%A A167297 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167296
%S A167296 1,0,4,0,12,0,20,0,16,0,36,0,44,0,48,0,60,0,68,0,80,0,84,0,144,0,64,0,
%T A167296 108,0,116,0,144,0,240,0,140,0,176,0,156,0,164,0,192,0,180,0,400,0
%N A167296 Totally multiplicative sequence with a(p) = 4*(p-2) for prime p.
%F A167296 Multiplicative with a(p^e) = (4*(p-2))^e. If n = Product p(k)^e(k) then a(n) = Product (4*(p(k)-2))^e(k). a(2k) = 0 for k >= 1. a(n) = A165825(n) * A166586(n) = 4^bigomega(n) * A166586(n) = 4^A001222(n) * A166586(n).
%K A167296 nonn,new
%O A167296 1,3
%A A167296 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167295
%S A167295 1,0,3,0,9,0,15,0,9,0,27,0,33,0,27,0,45,0,51,0,45,0,63,0,81,0,27,0,81,0,
%T A167295 87,0,81,0,135,0,105,0,99,0,117,0,123,0,81,0,135,0,225,0
%N A167295 Totally multiplicative sequence with a(p) = 3*(p-2) for prime p.
%F A167295 Multiplicative with a(p^e) = (3*(p-2))^e. If n = Product p(k)^e(k) then a(n) = Product (3*(p(k)-2))^e(k). a(2k) = 0 for k >= 1. a(n) = A165824(n) * A166586(n) = 3^bigomega(n) * A166586(n) = 3^A001222(n) * A166586(n).
%K A167295 nonn,new
%O A167295 1,3
%A A167295 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167294
%S A167294 1,0,2,0,6,0,10,0,4,0,18,0,22,0,12,0,30,0,34,0,20,0,42,0,36,0,8,0,54,0,
%T A167294 58,0,36,0,60,0,70,0,44,0,78,0,82,0,24,0,90,0,100,0
%N A167294 Totally multiplicative sequence with a(p) = 2*(p-2) for prime p.
%F A167294 Multiplicative with a(p^e) = (2*(p-2))^e. If n = Product p(k)^e(k) then a(n) = Product (2*(p(k)-2))^e(k). a(2k) = 0 for k >= 1. a(n) = A061142(n) * A166586(n) = 2^bigomega(n) * A166586(n) = 2^A001222(n) * A166586(n).
%K A167294 nonn,new
%O A167294 1,3
%A A167294 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009

%I A167293
%S A167293 4,15,21,35,55,77,91,99,117,143,153,171,187,209,221,247,253,299,323,325,
%T A167293 377,391,403,425,437,475,493,527,551,575,589,621,629,667,697,703,713,
%U A167293 725,775,779,783,817,837,851,899,925,943,957,989,999,1023,1025,1073
%N A167293 Long legs of Pythagorean triangles that are not divisible by any other long leg of a Pythagorean triangle.
%C A167293 All long legs of Pythagorean triangles (A009023) are multiples of these values, so these values can be thought of as "primes" of the sequence of long legs. This implies that A009023(n)/n is monotonically increasing; as it is also less than 1, it must converge to a constant. The constant is at least 22174/44545 ~ .4977, perhaps the constant is 1/2.
%o A167293 (PARI) llp = vector(60); np = 1; llp[np] = 4;
%o A167293 notdiv(k) = for(j=1,np,if(k%llp[j],NULL,return(0)));return(1);
%o A167293 for(k=4,1175,if(notdiv(k),if(isLongLeg(k),np+=1;llp[np]=k)))
%o A167293 for(n=1,60,print1(llp[n],", "))
%Y A167293 A009023
%K A167293 nonn,new
%O A167293 1,1
%A A167293 Gerald McGarvey (gerald.mcgarvey(AT)comcast.net), Nov 01 2009

%I A128209
%S A128209 1,2,2,4,6,12,22,44,86,172,342,684,1366,2732,5462,10924,21846,43692,
%T A128209 87382,174764,349526,699052,1398102,2796204,5592406,11184812,22369622,
%U A128209 44739244,89478486
%N A128209 Jacobsthal numbers(A001045)+1.
%C A128209 Row sums of A128208.
%C A128209 Essentially the same as A052953. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 14 2008
%F A128209 G.f.:(1-3*x^2)/(1-2*x-x^2+2*x^3); a(n)=1+2^n/3-(-1)^n/3;
%Y A128209 Cf. A167030, A153643 [Paul Curtz (bpcrtz(AT)free.fr), Oct 29 2009]
%K A128209 easy,nonn
%O A128209 0,2
%A A128209 Paul Barry (pbarry(AT)wit.ie), Feb 19 2007

%I A167167
%S A167167 1,1,1,3,5,11,21,43,85,171,341,683,1365,2731,5461,10923,21845,43691,87381,
%T A167167 174763,349525,699051,1398101,2796203,5592405,11184811,22369621,44739243,
%U A167167 89478485,178956971,357913941,715827883,1431655765,2863311531
%V A167167 -1,1,1,3,5,11,21,43,85,171,341,683,1365,2731,5461,10923,21845,43691,87381,
%W A167167 174763,349525,699051,1398101,2796203,5592405,11184811,22369621,44739243,
%X A167167 89478485,178956971,357913941,715827883,1431655765,2863311531
%N A167167 A001045 with a(0) replaced by -1.
%C A167167 Essentially the same as A154917, A001045, and perhaps also A152046.
%C A167167 Also the binomial transform of the sequence with terms (-1)^(n+1)*A128209(n).
%F A167167 a(n)=A001045(n), n>0.
%F A167167 a(n)+a(n+1) = 2*A001782(n) = 2*A131577(n) = A155559(n) = A090129(n+2), n>0.
%F A167167 G.f.: (2*x-1+2*x^2)/((1+x)*(1-2*x)).
%K A167167 sign,less,new
%O A167167 0,4
%A A167167 Paul Curtz (bpcrtz(AT)free.fr), Oct 29 2009
%E A167167 Edited and extended by R. J. Mathar (mathar(AT)strw.leidenuiv.nl), Nov 01 2009

%I A122429
%S A122429 13,9833,41647,151607,264757,356123,361223,446863,449093,457813,531383,
%T A122429 641057,655927,841697,855947,899263,913687,1052813,1081757,1379383,
%U A122429 1506493,1575757,1685087,1821013,1821377,1981517,2054233,2142037
%N A122429 Primes p such that q=4p^2+1, r=4q^2+1 and s=4r^2+1 are all primes.
%C A122429 Next terms up to 400000th prime are 2286877, 2524157, 2595247, 2621737, 2931583, 3023437, 3425843, 3428567, 3538517, 3705187, 3777883, 3799717, 3875143, 3913727, 3973553, 4019833, 4167073, 4249523, 4488167, 4651873, 4822193, 4914937, 5054167, 5108293, 5140147, 5465303, 5520007, 5542003 [Zak Seidov (zakseidov(AT)yahoo.com), Jan 16 2009]
%e A122429 13 is there because 13, 677, 1833317 and 13444204889957 are primes.
%t A122429 Reap[Do[p=Prime[n];q=4p^2+1;r=4q^2+1;s=4r^2+1;If[PrimeQ[{q,r,s}]=={True, True,True},Sow[p]],{n,15000}]][[2,1]]
%Y A122429 Cf. A052291, A005574, A001912.
%K A122429 nonn,new
%O A122429 1,1
%A A122429 Zak Seidov (zakseidov(AT)yahoo.com), Oct 20 2006
%E A122429 More terms from Don Reble (djr(AT)nk.ca), Oct 24 2006
%E A122429 Edited by R. J. Mathar, Nov 02 2009

%I A092626
%S A092626 13,17,29,31,43,47,59,67,71,79,83,97,127,137,157,173,229,239,251,263,
%T A092626 271,283,293,307,313,317,331,347,359,367,379,383,397,433,457,503,521,
%U A092626 547,563,571,587,593,653,673,677,739,743,751,787,797,823,827,853,857
%N A092626 Primes with one nonprime digit.
%e A092626 13 is prime and it has one nonprime digit, 1;
%e A092626 3259 is prime and it has one nonprime digit, 9.
%p A092626 stev_sez:=proc(n) local i, tren, st, ans, anstren; ans:=[ ]: anstren:=[ ]: tren:=n: for i while (tren>0) do st:=round( 10*frac(tren/10) ): ans:=[ op(ans), st ]: tren:=trunc(tren/10): end do; for i from nops(ans) to 1 by -1 do anstren:=[ op(anstren), op(i,ans) ]; od; RETURN(anstren); end:
%p A092626 ts_stnepf:=proc(n) local i, stpf, ans; ans:=stev_sez(n): stpf:=0: for i from 1 to nops(ans) do if (isprime(op(i,ans))='false') then stpf:=stpf+1; # number of nonprime digits fi od; RETURN(stpf) end:
%p A092626 ts_pr_neprn:=proc(n) local i, stpf, ans, ans1, tren; ans:=[ ]: stpf:=0: tren:=1: for i from 1 to n do if ( isprime(i)='true' and ts_stnepf(i) = 1) then ans:=[ op(ans), i ]: tren:=tren+1; fi od; RETURN(ans) end: ts_pr_neprn(4000);
%Y A092626 Cf. A019546.
%Y A092626 Cf. A141468 [Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Jan 19 2009]
%K A092626 nonn,base,new
%O A092626 1,1
%A A092626 Jani Melik (jani_melik(AT)hotmail.com), Apr 11 2004
%E A092626 Edited by R. J. Mathar, Nov 02 2009

%I A046363
%S A046363 6,10,12,22,28,34,40,45,48,52,54,56,58,63,75,76,80,82,88,90,96,99,104,
%T A046363 108,117,118,136,142,147,148,153,165,172,175,176,184,198,202,207,210,
%U A046363 214,224,245,248,250,252,268,273,274,279,294,296,298,300,316,320,325
%N A046363 Nonprime numbers whose sum of prime factors is prime (counted with multiplicity).
%C A046363 If prime numbers were included the sequence would be 2,3,5,6,7,10,11, 12,13,17,19,22,23,28,29,... which is A100118. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Oct 20 2007
%C A046363 Also: Composites with prime sum of prime factors. [Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Jan 20 2009]
%e A046363 214 = 2 * 107 -> Sum of factors is 109 -> 109 is prime.
%p A046363 ifac := proc (n) local L, x: L := ifactors(n)[2]: map(proc (x) options operator, arrow: seq(x[1], j = 1 .. x[2]) end proc, L) end proc: a := proc (n) if isprime(n) = false and isprime(add(t, t = ifac(n))) = true then n else end if end proc: seq(a(n), n = 1 .. 350); # with help from Edwin Clark [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 21 2009]
%t A046363 PrimeFactorsAdded[n_] := Plus @@ Flatten[Table[ #[[1]]*#[[2]], {1}] & /@ FactorInteger[n]]; GenerateA046363[n_] := Select[Range[n], PrimeQ[PrimeFactorsAdded[ # ]] && PrimeQ[ # ] == False &]; GenerateA046363[100] would give all elements of this sequence below 100. - Ryan Witko (witko(AT)nyu.edu), Mar 08 2004
%Y A046363 Cf. A046364, A046365, A100118, A000040, A002808.
%K A046363 nonn,new
%O A046363 1,1
%A A046363 Patrick De Geest (pdg(AT)worldofnumbers.com), Jun 15 1998.
%E A046363 Edited by R. J. Mathar, Nov 02 2009

%I A167151
%S A167151 0,1,2,3,4,7,5,12,6,18,8,26,9,35,10,45,11,56,13,69,14,83,15,98,16,114,
%T A167151 17,131,19,150,20,170,21,191,22,213,23,236,24,260,25,285,27,312,28,340,
%U A167151 29,369,30,399,31,430,32,462,33,495,34,529,36,565,37,602,38,640,39,679
%N A167151 a(2n+1)=a(2n)+a(2n-1), a(2n)=least number not yet in the sequence, a(1)=1.
%C A167151 Lexicographically first reordering of the nonnegative integers (can be extended by symmetry to a permutation of all integers) such that a(2n+1)=a(2n)+a(2n-1).
%H A167151 M. F. Hasler, <a href="b167151.txt">Table of n, a(n) for n=0,2000</a>.
%F A167151 a(2n-1)=A005228(n); a(2n)=A030124(n).
%o A167151 (PARI) {used=[]; print1(b=0); a=1; for(i=1,99, used=setunion(used,Set(a+=b)); while(setsearch(used,b++), used=setminus(used,Set(b))); print1(", "a", "b))}
%Y A167151 Cf. A022941, A143344, A156031.
%K A167151 easy,nonn,new
%O A167151 0,3
%A A167151 M. F. Hasler (MHasler(AT)univ-ag.fr), Nov 01 2009

%I A108067
%S A108067 8,8000000000,8000000008,8000000018,8018000000,8018000008,8018000018,8018018000,
%T A108067 8018018008,8018018018,8018018800,8018018808,8018018888,8018018880,8018018888,
%U A108067 8018018885,8018018884,8018018889,8018018881,8018018887,8018018886,8018018883,8018018882,8018018850
%N A108067 Integers in alphabetical order in U.S. English (another version of A004740).
%C A108067 The last term of this infinite sequence is 0. - Lekraj Beedassy (blekraj(AT)yahoo.com), Mar 09 2006
%e A108067 EIGHT
%e A108067 EIGHT BILLION
%e A108067 EIGHT BILLION EIGHT
%e A108067 EIGHT BILLION EIGHTEEN
%e A108067 EIGHT BILLION EIGHTEEN MILLION
%e A108067 EIGHT BILLION EIGHTEEN MILLION EIGHT
%e A108067 EIGHT BILLION EIGHTEEN MILLION EIGHTEEN
%e A108067 EIGHT BILLION EIGHTEEN MILLION EIGHTEEN THOUSAND
%e A108067 EIGHT BILLION EIGHTEEN MILLION EIGHTEEN THOUSAND EIGHT
%e A108067 EIGHT BILLION EIGHTEEN MILLION EIGHTEEN THOUSAND EIGHTEEN
%e A108067 EIGHT BILLION EIGHTEEN MILLION EIGHTEEN THOUSAND EIGHT HUNDRED
%e A108067 EIGHT BILLION EIGHTEEN MILLION EIGHTEEN THOUSAND EIGHT HUNDRED EIGHT
%e A108067 EIGHT BILLION EIGHTEEN MILLION EIGHTEEN THOUSAND EIGHT HUNDRED EIGHTEEN
%e A108067 EIGHT BILLION EIGHTEEN MILLION EIGHTEEN THOUSAND EIGHT HUNDRED EIGHTY
%e A108067 EIGHT BILLION EIGHTEEN MILLION EIGHTEEN THOUSAND EIGHT HUNDRED EIGHTY-EIGHT
%e A108067 EIGHT BILLION EIGHTEEN MILLION EIGHTEEN THOUSAND EIGHT HUNDRED EIGHTY-FIVE
%e A108067 EIGHT BILLION EIGHTEEN MILLION EIGHTEEN THOUSAND EIGHT HUNDRED EIGHTY-FOUR
%e A108067 EIGHT BILLION EIGHTEEN MILLION EIGHTEEN THOUSAND EIGHT HUNDRED EIGHTY-NINE
%e A108067 EIGHT BILLION EIGHTEEN MILLION EIGHTEEN THOUSAND EIGHT HUNDRED EIGHTY-ONE
%e A108067 EIGHT BILLION EIGHTEEN MILLION EIGHTEEN THOUSAND EIGHT HUNDRED EIGHTY-SEVEN
%e A108067 EIGHT BILLION EIGHTEEN MILLION EIGHTEEN THOUSAND EIGHT HUNDRED EIGHTY-SIX
%e A108067 EIGHT BILLION EIGHTEEN MILLION EIGHTEEN THOUSAND EIGHT HUNDRED EIGHTY-THREE
%e A108067 EIGHT BILLION EIGHTEEN MILLION EIGHTEEN THOUSAND EIGHT HUNDRED EIGHTY-TWO
%e A108067 EIGHT BILLION EIGHTEEN MILLION EIGHTEEN THOUSAND EIGHT HUNDRED FIFTY
%Y A108067 Cf. A004740.
%K A108067 nonn,word,new
%O A108067 1,1
%A A108067 Lekraj Beedassy (blekraj(AT)yahoo.com), May 31 2005
%E A108067 Corrections and additions from Matthew Goers (matthewgoers(AT)msn.com), Nov 02, 2009

%I A156031
%S A156031 1,2,3,5,4,9,6,15,7,22,8,30,10,40,11,51,12,63,13,76,14,90,16,106,17,123,
%T A156031 18,141,19,160,20,180,21,201,23,224,24,248,25,273,26,299,27,326,28,354,
%U A156031 29,383,31,414,32,446,33,479,34,513,35,548,36,584,37,621,38,659,39,698
%N A156031 Alternate A022941 and A143344.
%C A156031 Eric Angelini's definition was: start with 1,2,3; then alternately adjoin either the sum of the last two terms or the smallest number not yet in the sequence.
%H A156031 M. F. Hasler, <a href="b156031.txt">Table of n, a(n) for n=1,2001</a>.
%o A156031 (PARI) f="b156031.txt"; used=[]; write(f,c=1," ",b=1);a=1; for(i=1,1e3, used=setunion(used,Set(a+=b)); while(setsearch(used,b++), used=setminus(used,Set(b))); write(f,c++," "a"\n",c++," "b)) \\ [From M. F. Hasler, Nov 01 2009]
%Y A156031 Cf. A022941, A143344, A167151, A005228, A030124.
%K A156031 nonn,new
%O A156031 1,2
%A A156031 N. J. A. Sloane (njas(AT)research.att.com), Nov 01 2009, based on a posting by Eric Angelini to the Sequence Fans Mailing List.

%I A143344
%S A143344 1,3,4,6,7,8,10,11,12,13,14,16,17,18,19,20,21,23,24,25,26,27,28,29,31,65,
%T A143344 34,35,36,37,38,39,41,42,43,44,45,46,47,48,49,50,52,53,54,55,56,57,58
%N A143344 First differences of A022941.
%C A143344 This is (essentially) the sequence c() mentioned in the definition of A022941.
%Y A143344 Cf. A022941, A156031.
%K A143344 nonn,easy,more,new
%O A143344 1,2
%A A143344 N. J. A. Sloane (njas(AT)research.att.com), Nov 01 2009

%I A167292
%S A167292 1999,2999,4999,8999,13999,19991,19993,19997,25999,32999,35999,41999,
%T A167292 49991,49993,49999,52999,56999,59999,69991,69997,70999,71999,73999,
%U A167292 77999,79997,79999,85999,94999,98999,99901,99907,99923,99929,99961
%N A167292 Primes containing 999 as a substring.
%K A167292 nonn,new
%O A167292 1,1
%A A167292 Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 01 2009

%I A167290
%S A167290 8887,48883,48889,58889,68881,78887,78889,88801,88807,88811,88813,88817,
%T A167290 88819,88843,88853,88861,88867,88873,88883,88897,98887,108881,108883,
%U A167290 108887,138883,138889,158881,168887,178889,188801,188827,188831,188833
%N A167290 Primes containing 888 as a substring.
%K A167290 nonn,new
%O A167290 1,1
%A A167290 Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 01 2009

%I A167291
%S A167291 2,2,0,0,8,8,24,24,104,104,408,408
%V A167291 2,2,0,0,8,8,-24,-24,104,104,-408,-408
%N A167291 A137505=1,1,0,2,0,0,4,-4,4,4,-12,20,. a(n)=A137505(2n)+A137505(2n+1).
%F A167291 Double 2*(A109499=1,0,4,12,52,204,) signed. Note A137505(4n)=A137505(4n+1)=A109499 signed. A109499 is linked to A001045 via A109499(n+1)/4=0,1,3,13,51,=A015521 which inverse binomial transform is 0,1,1,7,13,55,=A015441, Fibonacci.
%K A167291 nonn,uned,new
%O A167291 0,1
%A A167291 Paul Curtz (bpcrtz(AT)free.fr), Nov 01 2009

%I A167289
%S A167289 1,2,1,3,2,1,4,3,2,1,5,4,3,2,1,6,5,4,3,2,1,7,6,5,4,3,2,8,1,7,6,5,4,3,9,
%T A167289 2,8,1,7,6,5,4,10,3,9,2,8,1,7,6,5,11,4,10,3,9,2,8,1,7,6,12,5,11,4,10,3,
%U A167289 9,2,8,1,7,13,6,12,5,11,4,10,3,9,2,8,14,1,7,13,6,12,5,11,4,10,3,9
%N A167289 Signature sequence of the Salem number 1.1883681475082235....
%D A167289 http://www.cecm.sfu.ca/~mjm/Lehmer/lists/SalemList.html
%t A167289 Clear[a, n, b]
%t A167289 a = {1 , -1 , 1, -1 , 0 , 0 , -1, 1, -1 }
%t A167289 b = Join[a, {1}, Reverse[a]]
%t A167289 p[x_] = Sum[b[[n]]*x^(n - 1), {n, 1, Length[b]}]
%t A167289 m = x /. Solve[p[x] == 0, x][[2]]
%t A167289 Take[Transpose[Sort[Flatten[Table[{i + j*m, i}, {i, 25}, {j, 17}], 1], #1[[1]] < #2[[1]] &]][[2]], 95]
%Y A167289 Cf. A147851, A073011
%K A167289 nonn,new
%O A167289 1,2
%A A167289 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 01 2009

%I A167288
%S A167288 1,2,1,3,2,1,4,3,2,1,5,4,3,2,1,6,5,4,3,2,1,7,6,5,4,3,2,8,1,7,6,5,4,3,9,
%T A167288 2,8,1,7,6,5,4,10,3,9,2,8,1,7,6,5,11,4,10,3,9,2,8,1,7,6,12,5,11,4,10,3,
%U A167288 9,2,8,1,7,13,6,12,5,11,4,10,3,9,2,8,1,14,7,13,6,12,5,11,4,10,3,9
%N A167288 Signature sequence of Salem number 1.1762808182599176...
%t A167288 Mathematica code based on that for A007337 by Robert G. Wilson v.:
%t A167288 m = x /. Solve[x^( 10) + x^9 - x^7 - x^6 - x^5 - x^4 - x^3 + x + 1 == 0, x][[2]]
%t A167288 Take[Transpose[Sort[Flatten[Table[{i + j*m, i}, {i, 25}, {j, 17}], 1], #1[[1]] < #2[[1]] &]][[2]], 95]
%Y A167288 Cf. A007337, A084531
%K A167288 nonn,new
%O A167288 1,2
%A A167288 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 01 2009

%I A167287
%S A167287 1,2,1,3,2,1,4,3,2,5,1,4,3,6,2,5,1,4,7,3,6,2,5,1,8,4,7,3,6,2,9,5,1,8,4,
%T A167287 7,3,10,6,2,9,5,1,8,4,11,7,3,10,6,2,9,5,12,1,8,4,11,7,3,10,6,13,2,9,5,
%U A167287 12,1,8,4,11,7,14,3,10,6,13,2,9,5,12,1,8,15,4,11,7,14,3,10,6,13,2,9,16
%N A167287 Signature sequence of Pisot number 1.3802775690976206...
%t A167287 m = x /. Solve[x^4 - x^3 - 1 == 0, x][[4]]
%t A167287 Take[Transpose[Sort[Flatten[Table[{i + j*m, i}, {i, 25}, {j, 17}], 1], #1[[1]] < #2[[1]] &]][[2]], 95]
%Y A167287 Cf. A007337, A084531
%K A167287 nonn,new
%O A167287 1,2
%A A167287 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 01 2009

%I A167286
%S A167286 1,2,1,3,2,1,4,3,2,1,5,4,3,2,6,1,5,4,3,7,2,6,1,5,4,8,3,7,2,6,1,5,9,4,8,
%T A167286 3,7,2,6,10,1,5,9,4,8,3,7,11,2,6,10,1,5,9,4,8,12,3,7,11,2,6,10,1,5,9,13,
%U A167286 4,8,12,3,7,11,2,6,10,14,1,5,9,13,4,8,12,3,7,11,15,2,6,10,14,1,5
%N A167286 Signature sequence of minimal Pisot number 1.3247179572447463...
%t A167286 m = x /. Solve[x^3 - x - 1 == 0, x][[1]]
%t A167286 Take[Transpose[Sort[Flatten[Table[{i + j*m, i}, {i, 25}, {j, 17}], 1], #1[[1]] < #2[[1]] &]][[2]], 95]
%Y A167286 Cf. A007337, A084531
%K A167286 nonn,new
%O A167286 1,2
%A A167286 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 01 2009

%I A167284
%S A167284 1,1,1,1,1,0,1,1,3,1,1,4,27,1,0,1,1,3,1,5,1,1,4,27,256,3125,1,0,1,4,27,
%T A167284 1,5,36,343,1,1,4,27,256,3125,1,7,64,0,1,4,27,1,5,36,343,1,9
%N A167284 A triangular sequence related to the EulerPhi function: t(n,k)=If[Mod[k, n] == 0 && (Mod[k, EulerPhi[n]] == 0), 1, Mod[k, n] ^ Mod[k, EulerPhi[n]]]
%C A167284 Row sums are:
%C A167284 {1, 2, 2, 6, 33, 12, 3414, 418, 3485, 427,...}
%C A167284 The sequences is related to indices solutions of:
%C A167284 x^k=Mod[a,n]
%D A167284 Burton, David M.,Elementary number theory,McGraw Hill,N.Y.,2002,pp173ff
%F A167284 t(n,k)=If[Mod[k, n] == 0 && (Mod[k, EulerPhi[n]] == 0), 1, Mod[k, n] ^ Mod[k, EulerPhi[n]]]
%e A167284 {1},
%e A167284 {1, 1},
%e A167284 {1, 1, 0},
%e A167284 {1, 1, 3, 1},
%e A167284 {1, 4, 27, 1, 0},
%e A167284 {1, 1, 3, 1, 5, 1},
%e A167284 {1, 4, 27, 256, 3125, 1, 0},
%e A167284 {1, 4, 27, 1, 5, 36, 343, 1},
%e A167284 {1, 4, 27, 256, 3125, 1, 7, 64, 0},
%e A167284 {1, 4, 27, 1, 5, 36, 343, 1, 9, 0}
%t A167284 t[n_, k_] = If[Mod[k, n] == 0 && (Mod[k, EulerPhi[n]] == 0), 1, Mod[k, n] ^ Mod[k, EulerPhi[n]]]
%t A167284 Flatten[Table[Table[t[n, k], {k, 1, n}], {n, 1, 10}]]
%K A167284 nonn,tabf,new
%O A167284 1,9
%A A167284 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 01 2009

%I A167283
%S A167283 46,74,94,106,134,158,166,178,194,226,254,262,314,326,334,346,422,446,
%T A167283 466,502,514,526,554,586,614,634,662,674,706,718,734,746,758,766,778,
%U A167283 794,802,818,878,886,898,914,934,958,974,982,998,1006,1018,1081,1082
%N A167283 Products of single (or isolated or non-twin) primes.
%e A167283 a(50)=1081 because 23*37=1081, where 23 is 2th non-twin prime and 37 is 3th non-twin prime.
%Y A167283 Cf. A007510, A037074, A085434.
%K A167283 nonn,new
%O A167283 1,1
%A A167283 Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Nov 01 2009, Nov 02 2009

%I A167282
%S A167282 1777,2777,11777,19777,22777,26777,27773,27779,41777,43777,44777,47777,
%T A167282 47779,50777,53777,57773,65777,67777,68777,71777,76777,77711,77713,
%U A167282 77719,77723,77731,77743,77747,77761,77773,77783,77797,79777,80777
%N A167282 Primes containing 777 as a substring.
%K A167282 nonn,base,new
%O A167282 1,1
%A A167282 Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 01 2009

%I A167281
%S A167281 5557,15551,15559,45553,45557,55501,55511,55529,55541,55547,55579,55589,
%T A167281 65551,65557,75553,75557,105557,115553,125551,135559,155501,155509,
%U A167281 155521,155537,155539,155557,155569,155579,155581,155593,155599,165551
%N A167281 Primes containing the string 555
%K A167281 nonn,base,new
%O A167281 1,1
%A A167281 Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 01 2009

%I A166582
%S A166582 4441,4447,14447,14449,24443,44417,44449,44453,44483,44491,44497,54443,
%T A166582 54449,74441,74449,84443,84449,94441,94447,124447,134443,144407,144409,
%U A166582 144413,144427,144439,144451,144461,144479,144481,144491,164443,164447
%N A166582 Primes containing the string 444
%K A166582 nonn,base,new
%O A166582 1,1
%A A166582 Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 01 2009

%I A166581
%S A166581 2333,3331,5333,7333,10333,13331,13337,13339,16333,17333,19333,20333,
%T A166581 23333,23339,29333,31333,33301,33311,33317,33329,33331,33343,33347,
%U A166581 33349,33353,33359,33377,33391,38333,41333,43331,49333,50333,55333
%N A166581 Primes containing the string 333
%K A166581 nonn,base,new
%O A166581 1,1
%A A166581 Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 01 2009

%I A166580
%S A166580 2221,12227,22229,22247,22259,22271,22273,22277,22279,22283,22291,42221,
%T A166580 42223,42227,52223,72221,72223,72227,72229,82223,92221,92227,102229,
%U A166580 112223,122201,122203,122207,122209,122219,122231,122251,122263,122267
%N A166580 Prime numbers containing the string 222
%K A166580 nonn,base,new
%O A166580 1,1
%A A166580 Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 01 2009

%I A167280
%S A167280 0,0,1,2,4,7,4,8,7,4,8,5,0,0,1,2,4,7,4,8,7,4,8,5,0,0,1,2,4,7,4,8,7,4,8,
%T A167280 5,0,0,1,2,4,7,4,8,7,4,8,5,0,0,1,2,4,7,4,8,7,4,8,5,0,0,1,2,4,7,4,8,7,4,
%U A167280 8,5,0,0,1,2,4,7,4,8,7,4,8,5,0,0,1,2,4,7,4,8,7,4,8,5,0,0,1,2,4,7,4,8,7
%N A167280 Periodic sequence a(n) for which sum of terms of a(n)*2^n mod 10 is 50. First case of period 12:repeat 0,0,1,2,4,7,4,8,7,4,8,5. Third column is A000689.
%C A167280 b(n)=0,0,1,2,4,7,14,28,57,114,228,455,910,1820,3641,7282,14564, is original A113405, Barry,2005.Third 0 added Aug 05 2007. a(n)= ( b(n)=A113405(n+1) mod 10 ). Ordered:0,0,1,2,4,4,4,5,7,7,8,8. See A141425. a(n)+a(n+6)= period 6:repeat 4,8,8,6,12,12. See A004523.
%Y A167280 A000071, A000076.
%K A167280 nonn,uned,new
%O A167280 0,4
%A A167280 Paul Curtz (bpcrtz(AT)free.fr), Nov 01 2009

%I A166579
%S A166579 17,173,179,317,617,1117,1171,1217,1709,1721,1723,1733,1741,1747,1753,
%T A166579 1759,1777,1783,1787,1789,2017,2179,2417,2617,2917,3217,3517,3617,3917,
%U A166579 4177,4217,4517,4817,5171,5179,5417,5717,6173,6217,6317,6917,7177,7417
%N A166579 Prime numbers containing the string 17
%K A166579 nonn,new
%O A166579 1,1
%A A166579 Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 01 2009

%I A166573
%S A166573 13,113,131,137,139,613,1013,1213,1301,1303,1307,1319,1321,1327,1361,
%T A166573 1367,1373,1381,1399,1613,1913,2113,2131,2137,2213,2713,3137,3313,3413,
%U A166573 3613,4013,4133,4139,4513,4813,5113,5413,5813,6113,6131,6133,7013,7213
%N A166573 Prime numbers containing the string 13
%K A166573 nonn,new
%O A166573 1,1
%A A166573 Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 01 2009

%I A167279
%S A167279 0,1,1,0,2,0,1,3,3,1,0,4,0,4,0,1,5,19,19,5,1,0,6,0,70,0,6,0,1,7,85,245,
%T A167279 245,85,7,1,0,8,0,856,0,856,0,8,0,1,9,355,2967,8171,8171,2967,355,9,1,0,
%U A167279 10,0,10164,0,80518,0,10164,0,10,0,1,11,1435,34463,277969
%N A167279 Square array read by antidiagonals: T(n,m) = number of ways to partition an nXm grid into 2 connected equal-area regions.
%K A167279 nonn,tabl,new
%O A167279 1,5
%A A167279 Ron Hardin (rhhardin(AT)att.net), Nov 01 2009

%I A167278
%S A167278 3,29,41,53,59,71,83,89,97,101,127,131,137,163,167,173,179,223,229,239,
%T A167278 257,263,269,281,307,311,331,337,347,359,367,373,379,383,389,397,401,
%U A167278 409,419,443,449,457,461,479,487,491,499,503,509,521,547,557,563,569
%N A167278 Smallest prime>nth single (or isolated or non-twin) prime.
%Y A167278 Cf. A000040, A007510.
%K A167278 nonn,new
%O A167278 1,1
%A A167278 Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Nov 01 2009

%I A167277
%S A167277 1,22,36,46,52,66,78,82,88,96,112,126,130,156,162,166,172,210,222,232,
%T A167277 250,256,262,276,292,306,316,330,336,352,358,366,372,378,382,388,396,
%U A167277 400,408,438,442,448,456,466,478,486,490,498,502,508,540,546,556,562
%N A167277 Largest nonprime<nth single (or isolated or non-twin) prime.
%C A167277 Or, nth single prime minus smallest divisor of nth single prime.
%Y A167277 Cf. A007510, A018252.
%K A167277 nonn,new
%O A167277 1,2
%A A167277 Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Nov 01 2009

%I A167276
%S A167276 7,13,17,23,31,37,41,43,47,53,67,73,83,89,107,109,157,233,241,421,463
%N A167276 Primes p such that p^2=x^2+y^2-1 with x and y also prime.
%C A167276 Appears to be infinite.
%e A167276 a(1)=7 (x=5, y=5); a(2)=13 (x=7, y=11); a(3)=17 (x=11, y=17); a(4)=23 (x=13, y=19); a(5)=31 (x=11, y=31);...; a(21)=463 (x=461, y=43)
%e A167276 a(1)=13 (x=7, y=11); a(2)=17 (x=11, y=13); a(3)=23 (x=13, y=19); a(4)=31 (x=11, y=29). [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 02 2009]
%Y A167276 Cf. A000040.
%K A167276 nonn,new
%O A167276 1,1
%A A167276 Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Nov 01 2009
%E A167276 Edited and extended by Daniel Platt, Nov 02 2009

%I A167236
%S A167236 2,7,16,23,37,59,97,149,211,307,907,1151,1361,5623,8501,9587,15727,
%T A167236 19661,31469,156007,360749,370373,492227,1349651,1357333,2010881,
%U A167236 4652507,17051887,20831533,47326913,122164969,189695893,191913031
%N A167236 Larger prime power associated with gaps in A167235.
%H A167236 Donovan Johnson, <a href="b002540.txt">Table of n, a(n) for n=1..79</a> used to calculate terms.
%e A167236 59 is in the sequence since 53 and 59 are consecutive prime powers with a difference of 6 and no smaller pair of consecutive prime powers differ by 6 or more.
%o A167236 (PARI) isA000961(n) = (omega(n) == 1 | n == 1)
%o A167236 d_max=0;n_prev=1;for(n=2,1e6,if(isA000961(n),d=n-n_prev;if(d>d_max,print(n);d_max=d);n_prev=n))
%Y A167236 Size of gap: A167235
%Y A167236 Smaller prime power (start of gap): A002540
%Y A167236 Gaps between prime powers: A057820
%Y A167236 List of prime powers: A000961
%K A167236 nonn,new
%O A167236 1,1
%A A167236 Michael Porter (michael_b_porter(AT)yahoo.com), Nov 01 2009

%I A167235
%S A167235 1,2,3,4,5,6,8,10,12,14,20,22,30,32,34,36,44,52,72,86,96,112,114,118,
%T A167235 132,148,154,180,210,220,222,234,248,250,282,288,292,320,336,354,382,
%U A167235 384,394,456,464,468,474,486,490,500,514,516,532,534,540,582,588,602
%N A167235 Record gaps between prime powers (A000961).
%H A167235 Donovan Johnson, <a href="b002540.txt">Table of n, a(n) for n=1..79</a> used to calculate terms.
%e A167235 6 is in the sequence since 53 and 59 are consecutive prime powers and no smaller pair of consecutive prime powers differ by 6 or more.
%o A167235 (PARI) isA000961(n) = (omega(n) == 1 | n == 1)
%o A167235 d_max=0;n_prev=1;for(n=2,1e6,if(isA000961(n),d=n-n_prev;if(d>d_max,print(d);d_max=d);n_prev=n))
%Y A167235 Smaller prime power (start of gap): A002540
%Y A167235 Larger prime power (end of gap): A167236
%Y A167235 Gaps between prime powers: A057820
%Y A167235 List of prime powers: A000961
%K A167235 nonn,new
%O A167235 1,2
%A A167235 Michael Porter (michael_b_porter(AT)yahoo.com), Nov 01 2009

%I A167189
%S A167189 4,8,16,25,49,121,169,243,512,1331,1681,2809,4913,6241,7921,9409,14641,
%T A167189 22201,36481,44521,49729,94249,185761,226981,271441,292681,452929,
%U A167189 619369,769129,822649,1181569,1852321,5442889,6265009,8994001,10883401
%N A167189 Larger prime power associated with record gap in A167186.
%e A167189 49 is in the sequence since the gap between it the previous prime power, 32, is greater than any previous gap.
%o A167189 (PARI) isA025475(n) = (omega(n) == 1 & !isprime(n)) | (n == 1)
%o A167189 d_max=0;n_prev=1;for(n=2,32e6,if(isA025475(n),d=n-n_prev;if(d>d_max,print(n);d_max=d);n_prev=n))
%Y A167189 Smaller prime power is in A167188
%Y A167189 Record gaps between non-prime prime powers: A167186
%Y A167189 Gaps between non-prime prime powers: A053707
%Y A167189 List of non-prime prime powers: A025475
%K A167189 nonn,new
%O A167189 1,1
%A A167189 Michael Porter (michael_b_porter(AT)yahoo.com), Nov 01 2009

%I A167188
%S A167188 1,4,9,16,32,81,128,169,361,1024,1369,2401,4489,5329,6889,8192,12769,
%T A167188 19683,32768,39601,44521,85849,177241,218089,262144,279841,436921,
%U A167188 597529,744769,786769,1142761,1771561,5340721,6135529,8826841,10699441
%N A167188 Smaller prime power associated with record gap in A167186.
%e A167188 32 is in the sequence since the gap between 32 and the next prime power, 49, is greater than any previous gap.
%o A167188 (PARI) isA025475(n) = (omega(n) == 1 & !isprime(n)) | (n == 1)
%o A167188 d_max=0;n_prev=1;for(n=2,32e6,if(isA025475(n),d=n-n_prev;if(d>d_max,print(n_prev);d_max=d);n_prev=n))
%Y A167188 Larger prime power: A167189
%Y A167188 Record gaps between non-prime prime powers: A167186
%Y A167188 Gaps between non-prime prime powers: A053707
%Y A167188 List of non-prime prime powers: A025475
%K A167188 nonn,new
%O A167188 1,2
%A A167188 Michael Porter (michael_b_porter(AT)yahoo.com), Nov 01 2009

%I A166572
%S A166572 11,113,211,311,811,911,1103,1109,1117,1123,1129,1151,1153,1163,1171,
%T A166572 1181,1187,1193,1511,1811,2011,2111,2113,2311,2411,2711,3011,3119,3511,
%U A166572 3911,4111,4211,5011,5113,5119,5711,6011,6113,6211,6311,6911,7211,7411
%N A166572 Prime numbers containing the string 11
%K A166572 nonn,base,new
%O A166572 1,1
%A A166572 Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 01 2009

%I A166571
%S A166571 101,103,107,109,1009,1013,1019,1021,1031,1033,1039,1049,1051,1061,1063,
%T A166571 1069,1091,1093,1097,1103,1109,3109,5101,5107,6101,7103,7109,8101,9103,
%U A166571 9109,10007,10009,10037,10039,10061,10067,10069,10079,10091,10093,10099
%N A166571 Prime numbers containing the string 10
%K A166571 nonn,base,new
%O A166571 1,1
%A A166571 Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 01 2009

%I A167275
%S A167275 1,4,4,8,4,8,8,16,4,8,8,16,8,16,16,32,4,8,8,16,8,16,16,32
%N A167275 Row sums of triangle A167274 (a variant of Gould's sequence A001316).
%F A167275 Given Gould's sequence, A001316, (1, 2, 2, 4, 2, 4, 4, 8,...); for a(n)>1,
%F A167275 a(n) = 2*A001316(n).
%e A167275 a(3) = 8 = 2*A001316 = 2*4. a(3) = 8 = (1 + 3 + 3 + 1); where (1, 3, 3, 1) = row 3 of triangle A167274.
%Y A167275 Cf. A167274
%K A167275 nonn,new
%O A167275 0,2
%A A167275 Gary W. Adamson & Mats Granvik (qntmpkt(AT)yahoo.com), Oct 31 2009

%I A167274
%S A167274 1,3,1,3,0,1,1,3,3,1,3,0,0,0,1,1,3,0,0,3,1,1,0,3,0,3,0,1,3,1,1,3,1,3,3,
%T A167274 1,3,0,0,0,0,0,0,0,1,1,3,0,0,0,0,0,0,3,1,1,0,3,0,0,0,0,0,3,0,1,3,1,1,3,
%U A167274 0,0,0,0,1,3,3,1
%N A167274 Triangle by rows, = 2*A047999 - A047999^(-1); = twice Sierpinski's gasket minus the inverse of Sierpinski's gasket.
%C A167274 Row sums = A167275: (1, 4, 4, 8, 4, 8, 8,...).
%F A167274 Let Sierpinski's gasket, A047999 = S; as an infinite lower triangular matrix.
%F A167274 A167274 = 2*S - 1/S.
%e A167274 First few rows of the triangle =
%e A167274 1;
%e A167274 3, 1;
%e A167274 3, 0, 1;
%e A167274 1, 3, 3, 1;
%e A167274 3, 0, 0, 0, 1;
%e A167274 1, 3, 0, 0, 3, 1;
%e A167274 1, 0, 3, 0, 3, 0, 1;
%e A167274 3, 1, 1, 3, 1, 3, 3, 1;
%e A167274 3, 0, 0, 0, 0, 0, 0, 0, 1;
%e A167274 1, 3, 0, 0, 0, 0, 0, 0, 3, 1;
%e A167274 1, 0, 3, 0, 0, 0, 0, 0, 3, 0, 1;
%e A167274 3, 1, 1, 3, 0, 0, 0, 0, 1, 3, 3, 1;
%e A167274 1, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 1;
%e A167274 3, 1, 0, 0, 1, 3, 0, 0, 1, 3, 0, 0, 3, 1;
%e A167274 3, 0, 1, 0, 1, 0, 3, 0, 1, 0, 3, 0, 3, 0, 1
%e A167274 1, 3, 3, 1, 3, 1, 1, 3, 3, 1, 1, 3, 1, 3, 3, 1;
%e A167274 ...
%Y A167274 Cf. A047999, A167275
%K A167274 nonn,new
%O A167274 0,2
%A A167274 Gary W. Adamson & Mats Granvik (qntmpkt(AT)yahoo.com), Oct 31 2009

%I A167273
%S A167273 1,1,3,4,10,13,28,37,73,97,177,236,412,548,915,1218,1971,2616,4117,5453,
%T A167273 8390,11082,16710,22012,32638,42864,62592,81972,118125
%N A167273 Infinite product of Triangle A167271 columns
%F A167273 Infinite product of triangle A167271 columns, as polynomials: (1, 1, 1,...)
%F A167273 * (1, 0, 2, 0, 3,...) * (1, 0, 0, 1, 0, 0, 1,...) * (1, 0, 0, 3, 0, 0, 6,...)
%F A167273 * ...
%Y A167273 Cf. A167271
%K A167273 nonn,new
%O A167273 0,3
%A A167273 Gary W. Adamson & Mats Granvik (qntmpkt(AT)yahoo.com), Oct 31 2009

%I A167272
%S A167272 1,2,2,4,2,6,2,9,3,8,2,19,2,10,5,25,2,23,2,34,4,14,2,78,3,16,4,53,2,76,
%T A167272 2,98
%N A167272 Row sums of triangle A167271
%e A167272 a(5) = 6 = ((1 + 3 + 1 + 0 + 0 + 1)
%Y A167272 Cf. A167271
%K A167272 nonn,new
%O A167272 0,2
%A A167272 Gary W. Adamson & Mats Granvik (qntmpkt(AT)yahoo.com), Oct 31 2009

%I A167271
%S A167271 1,1,1,1,0,1,1,2,0,1,1,0,0,0,1,1,3,1,0,0,1,1,0,0,0,0,0,1,1,4,0,3,0,0,0,
%T A167271 1,1,0,1,0,0,0,0,0,1,1,5,0,0,1,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,1,1,6,1,6,
%U A167271 0,4,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1
%N A167271 Triangle by rows, A167269 columns aerated with k zeros
%C A167271 Row sums = A167272: (1, 2, 2, 4, 2, 6, 2, 9,k 3, 8, 2, 19,...).
%C A167271 Product of columns = A167273: (1, 1, 3, 4, 10, 13, 28, 37, 73,...).
%F A167271 Given triangle A167269, T(n,k), aerate column terms with k zeros.
%e A167271 First few rows of the triangle =
%e A167271 1,
%e A167271 1, 1;
%e A167271 1, 0, 1;
%e A167271 1, 2, 0, 1;
%e A167271 1, 0, 0, 0, 1;
%e A167271 1, 3, 1, 0, 0, 1;
%e A167271 1, 0, 0, 0, 0, 0, 1;
%e A167271 1, 4, 0, 3, 0, 0, 0, 1;
%e A167271 1, 0, 1, 0, 0, 0, 0, 0, 1;
%e A167271 1, 5, 0, 0, 1, 0, 0, 0, 0, 1;
%e A167271 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
%e A167271 1, 6, 1, 6, 0, 4, 0, 0, 0, 0, 0, 1;
%e A167271 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
%e A167271 1, 7, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1;
%e A167271 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
%e A167271 1, 8, 0, 10, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 1;
%e A167271 ...
%Y A167271 Cf. A167269, A167272, A167273
%K A167271 nonn,tabl,new
%O A167271 0,8
%A A167271 Gary W. Adamson & Mats Granvik (qntmpkt(AT)yahoo.com), Oct 31 2009

%I A086239
%S A086239 3,3,4,9,8,1,3,2,5,2,9,9,9,9,3,1,8,1,0,6,3,3,1,7,1,2,1,4,8,7,5,4,3,5,7,
%T A086239 3,7,7,9,9,7,5,3,8,0,7,5,5,0,7,7,0,4,8,1,0,8,0,2,0,5,7,8,8,4,5,2,2,2,8,
%U A086239 4,3,2,7,1,8,8,4,1,1,0,6,2,4,8,9,9,6,3,1,0,2,9,8,0,3,3,4,5,3,9,2,4,8,6
%N A086239 Decimal expansion of sum(c[k]/prime[k], k=2..infinity), where c[k]=-1 if p==1 (mod 4) and c[k]=+1 if p==3 (mod 4).
%C A086239 This is sum_{p prime, p>=3} -(-4/p)/p where (-4/.) is the Legendre symbol and is equal to - L(1,(-4/.)) plus an absolutely convergent sum (and therefore converges).
%D A086239 Henri Cohen, "High Precision Computation of Hardy-Littlewood Constants", preprint (1991), http://www.math.u-bordeaux.fr/~cohen/hardylw.dvi [From M. F. Hasler (MHasler(AT)univ-ag.fr), Oct 29 2009]
%D A086239 S. R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, pp. 94-98
%H A086239 D. Broadhurst, <a href="http://tech.groups.yahoo.com/group/primenumbers/message/21083">post in primenumbers group</a>, Oct 29 2009 [From M. F. Hasler (MHasler(AT)univ-ag.fr), Oct 29 2009]
%H A086239 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeSums.html">PrimeSums</a>
%e A086239 0.33498132529999...
%o A086239 (PARI) /* the given number of primes and terms in the sum yield over 105 correct digits */ { P=vector(15, k, (2-prime(k)%4)/prime(k)); -sum(s=1,60, moebius(s)/s*log( prod( k=2, #P, 1-P[k]^s, if(s%2, if(s==1, Pi/4, sumalt(k=0,(-1)^k/(2*k+1)^s)) ,zeta(s)*(1-1/2^s) ))), sum(k=2,#P, P[k], .))} \\ [From M. F. Hasler (MHasler(AT)univ-ag.fr), Oct 29 2009]
%K A086239 nonn,cons,new
%O A086239 0,1
%A A086239 Eric Weisstein (eric(AT)weisstein.com), Jul 13, 2003
%E A086239 Edited by N. J. A. Sloane (njas(AT)research.att.com), Jun 10 2008
%E A086239 Corrected a(9) and example, added a(10)-a(104) following Broadhurst and Cohen. - M. F. Hasler, Oct 29 2009

%I A167265
%S A167265 0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,41,0,0,41,0,
%T A167265 0,1,0,0,0,0,0,0,0,1,0,55,0,0,0,0,0,0,55,0,0,0,3127,0,0,178939,0,0,3127,
%U A167265 0,0,0,0,0,179399,0,0,0,0,179399,0,0,0,0,0,0,0,13205354,0,0,0,13205354,0
%N A167265 T(n,m) = Number of ways to partition an nXm grid into 9 connected equal-area regions.
%H A167265 R. H. Hardin, <a href="b167265.txt">Table of n, a(n) for n=1..127</a>
%K A167265 nonn,tabl,new
%O A167265 1,31
%A A167265 Ron Hardin (rhhardin(AT)att.net) Oct 31 2009

%I A167264
%S A167264 0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,36,0,0,0,1,0,0,0,0,0,0,
%T A167264 1,0,34,0,939,0,939,0,34,0,0,0,1173,0,0,0,0,1173,0,0,0,0,0,40899,0,0,0,
%U A167264 40899,0,0,0,0,0,0,0,1696781,0,0,1696781,0,0,0,0,0,153,0,890989,0
%N A167264 T(n,m) = Number of ways to partition an nXm grid into 8 connected equal-area regions.
%H A167264 R. H. Hardin, <a href="b167264.txt">Table of n, a(n) for n=1..112</a>
%K A167264 nonn,tabl,new
%O A167264 1,25
%A A167264 Ron Hardin (rhhardin(AT)att.net) Oct 31 2009

%I A167263
%S A167263 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,21,0,0,0,0,21,
%T A167263 0,0,0,441,0,0,0,441,0,0,0,0,0,9157,0,0,9157,0,0,0,0,0,0,0,214689,0,
%U A167263 214689,0,0,0,0,0,0,0,0,0,5850115,5850115,0,0,0,0,0,0,0,0,0,0,0
%N A167263 T(n,m) = Number of ways to partition an nXm grid into 7 connected equal-area regions.
%H A167263 R. H. Hardin, <a href="b167263.txt">Table of n, a(n) for n=1..111</a>
%K A167263 nonn,tabl,new
%O A167263 1,30
%A A167263 Ron Hardin (rhhardin(AT)att.net) Oct 31 2009

%I A167262
%S A167262 0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,1,0,11,11,0,1,0,13,0,0,0,13,0,0,0,170,0,0,
%T A167262 170,0,0,0,0,0,2003,0,2003,0,0,0,0,41,997,0,27950,27950,0,997,41,0,0,0,0,
%U A167262 0,0,451206,0,0,0,0,0,1,0,7670,244252,0,6633399,6633399,0,244252,7670,0
%N A167262 T(n,m) = Number of ways to partition an nXm grid into 6 connected equal-area regions.
%H A167262 R. H. Hardin, <a href="b167262.txt">Table of n, a(n) for n=1..110</a>
%K A167262 nonn,tabl,new
%O A167262 1,18
%A A167262 Ron Hardin (rhhardin(AT)att.net) Oct 31 2009

%I A167261
%S A167261 0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,8,0,0,8,0,0,0,62,0,62,0,0,0,0,0,454,454,
%T A167261 0,0,0,0,0,0,0,4006,0,0,0,0,1,0,0,0,33344,33344,0,0,0,1,0,64,0,0,270827,
%U A167261 0,270827,0,0,64,0,0,0,8072,0,2152050,0,0,2152050,0,8072,0,0,0,0,0
%N A167261 T(n,m) = Number of ways to partition an nXm grid into 5 connected equal-area regions.
%H A167261 R. H. Hardin, <a href="b167261.txt">Table of n, a(n) for n=1..110</a>
%K A167261 nonn,tabl,new
%O A167261 1,17
%A A167261 Ron Hardin (rhhardin(AT)att.net) Oct 31 2009

%I A167260
%S A167260 0,0,0,0,1,0,1,0,0,1,0,5,0,5,0,0,0,23,23,0,0,0,11,0,117,0,11,0,1,0,0,501,
%T A167260 501,0,0,1,0,25,0,2369,0,2369,0,25,0,0,0,1038,9525,0,0,9525,1038,0,0,0,
%U A167260 45,0,39731,0,442791,0,39731,0,45,0,1,0,0,145415,1596459,0,0,1596459
%N A167260 T(n,m) = Number of ways to partition an nXm grid into 4 connected equal-area regions.
%H A167260 R. H. Hardin, <a href="b167260.txt">Table of n, a(n) for n=1..83</a>
%K A167260 nonn,tabl,new
%O A167260 1,12
%A A167260 Ron Hardin (rhhardin(AT)att.net) Oct 31 2009

%I A167259
%S A167259 0,0,0,1,0,1,0,3,3,0,0,0,10,0,0,1,0,23,23,0,1,0,9,56,0,56,9,0,0,0,132,0,
%T A167259 0,132,0,0,1,0,259,1787,0,1787,259,0,1,0,19,546,0,22889,22889,0,546,19,0,
%U A167259 0,0,1095,0,0,264500,0,0,1095,0,0,1,0,2043,72105,0
%N A167259 T(n,m) = Number of ways to partition an nXm grid into 3 connected equal-area regions.
%K A167259 nonn,tabl,new
%O A167259 1,8
%A A167259 Ron Hardin (rhhardin(AT)att.net) Oct 31 2009

%I A167258
%S A167258 1,34,1173,40899,1696781,81459922,3825111851
%N A167258 Number of ways to partition a n X 8 grid into 8 connected equal-area regions
%e A167258 Some solutions for n=3
%e A167258 ...1.1.2.3.3.4.4.4...1.2.3.3.3.4.4.4...1.2.2.2.3.3.3.4...1.1.2.3.4.5.5.6
%e A167258 ...1.2.2.5.3.6.6.7...1.2.5.6.6.7.8.8...1.1.5.5.6.7.7.4...1.2.2.3.4.5.7.6
%e A167258 ...8.8.8.5.5.6.7.7...1.2.5.5.6.7.7.8...8.8.8.5.6.6.7.4...8.8.8.3.4.7.7.6
%e A167258 ------
%e A167258 ...1.2.2.2.3.3.4.4...1.1.2.3.3.4.5.5...1.1.2.2.3.4.5.5...1.1.1.2.3.3.3.4
%e A167258 ...1.5.6.6.3.7.8.4...1.6.2.3.7.4.5.8...6.1.2.7.3.4.8.5...5.5.5.2.6.6.4.4
%e A167258 ...1.5.5.6.7.7.8.8...6.6.2.7.7.4.8.8...6.6.7.7.3.4.8.8...7.7.7.2.6.8.8.8
%e A167258 ------
%e A167258 ...1.1.2.2.3.4.5.5...1.1.1.2.2.2.3.3...1.2.3.3.3.4.5.5...1.2.3.3.4.5.5.5
%e A167258 ...1.6.2.7.3.4.8.5...4.4.4.5.6.6.3.7...1.2.2.6.6.4.7.5...1.2.3.6.4.7.7.8
%e A167258 ...6.6.7.7.3.4.8.8...8.8.8.5.5.6.7.7...1.8.8.8.6.4.7.7...1.2.6.6.4.7.8.8
%e A167258 ------
%e A167258 ...1.2.3.4.4.5.6.6...1.1.2.3.4.4.5.6...1.1.2.3.3.3.4.4...1.1.2.2.2.3.4.4
%e A167258 ...1.2.3.4.7.5.8.6...1.7.2.3.4.8.5.6...5.1.2.6.7.7.4.8...5.1.6.7.7.3.4.8
%e A167258 ...1.2.3.7.7.5.8.8...7.7.2.3.8.8.5.6...5.5.2.6.6.7.8.8...5.5.6.6.7.3.8.8
%K A167258 nonn,new
%O A167258 1,2
%A A167258 Ron Hardin (rhhardin(AT)att.net) Oct 31 2009

%I A167257
%S A167257 1,25,1038,39731,1596459
%N A167257 Number of ways to partition a n X 8 grid into 4 connected equal-area regions
%e A167257 Some solutions for n=3
%e A167257 ...1.1.1.1.1.2.3.3...1.2.2.2.2.2.3.4...1.1.1.1.2.3.3.3...1.1.1.2.2.2.2.2
%e A167257 ...1.4.2.2.2.2.2.3...1.1.2.3.3.3.3.4...1.2.2.2.2.4.4.3...1.3.1.2.4.4.4.4
%e A167257 ...4.4.4.4.4.3.3.3...1.1.1.3.4.4.4.4...1.2.4.4.4.4.3.3...1.3.3.3.3.3.4.4
%e A167257 ------
%e A167257 ...1.2.2.2.2.3.3.3...1.2.2.2.3.3.3.3...1.1.1.2.2.3.3.3...1.2.2.3.3.3.3.3
%e A167257 ...1.2.2.4.4.4.3.3...1.2.2.2.4.4.3.3...4.1.1.1.2.2.3.3...1.1.2.2.3.4.4.4
%e A167257 ...1.1.1.1.4.4.4.3...1.1.1.1.4.4.4.4...4.4.4.4.4.2.2.3...1.1.1.2.2.4.4.4
%e A167257 ------
%e A167257 ...1.1.1.1.2.2.2.2...1.1.1.2.2.2.3.3...1.2.2.2.2.3.4.4...1.1.1.1.1.2.2.3
%e A167257 ...1.3.1.4.4.4.4.2...1.2.2.2.3.3.3.3...1.2.2.3.3.3.3.4...1.4.4.4.2.2.3.3
%e A167257 ...3.3.3.3.3.4.4.2...1.1.4.4.4.4.4.4...1.1.1.1.3.4.4.4...4.4.4.2.2.3.3.3
%e A167257 ------
%e A167257 ...1.1.2.2.3.4.4.4...1.1.2.3.3.3.3.3...1.1.1.1.2.2.3.3...1.1.2.2.3.4.4.4
%e A167257 ...1.1.2.2.3.4.4.4...1.1.2.2.4.4.3.4...4.1.1.4.2.2.3.3...1.2.2.2.3.4.4.4
%e A167257 ...1.1.2.2.3.3.3.3...1.1.2.2.2.4.4.4...4.4.4.4.2.2.3.3...1.1.1.2.3.3.3.3
%K A167257 nonn,new
%O A167257 1,2
%A A167257 Ron Hardin (rhhardin(AT)att.net) Oct 31 2009

%I A167256
%S A167256 1,8,355,10164,277969
%N A167256 Number of ways to partition a n X 8 grid into 2 connected equal-area regions
%e A167256 Some solutions for n=3
%e A167256 ...1.1.1.1.2.2.2.2...1.1.1.1.1.1.1.1...1.1.1.1.1.1.1.1...1.1.1.1.1.1.1.1
%e A167256 ...1.2.2.2.2.1.2.2...2.1.1.2.2.1.1.2...1.2.2.2.1.2.2.1...2.2.1.2.2.2.1.1
%e A167256 ...1.1.1.1.1.1.2.2...2.2.2.2.2.2.2.2...1.2.2.2.2.2.2.2...2.2.2.2.2.2.2.1
%e A167256 ------
%e A167256 ...1.1.2.2.2.2.2.2...1.1.1.1.1.2.2.2...1.1.1.2.2.2.2.2...1.1.1.1.1.1.1.2
%e A167256 ...1.1.1.1.1.1.2.2...1.1.1.1.2.2.2.2...1.1.1.2.2.2.2.2...1.2.2.1.1.2.1.2
%e A167256 ...1.1.1.1.2.2.2.2...1.1.1.2.2.2.2.2...1.1.1.1.1.1.2.2...1.2.2.2.2.2.2.2
%e A167256 ------
%e A167256 ...1.1.1.1.1.1.1.2...1.1.1.1.1.1.1.2...1.2.2.2.2.2.2.2...1.1.1.1.1.1.1.1
%e A167256 ...1.2.2.1.2.2.1.2...2.1.1.1.1.2.1.2...1.2.2.1.1.2.1.2...1.2.2.1.2.1.2.1
%e A167256 ...1.1.2.2.2.2.2.2...2.2.2.2.2.2.2.2...1.1.1.1.1.1.1.2...2.2.2.2.2.2.2.2
%e A167256 ------
%e A167256 ...1.1.1.1.1.1.1.2...1.1.1.1.1.1.2.2...1.1.1.1.1.1.1.1...1.1.2.2.2.2.2.2
%e A167256 ...1.1.2.1.1.2.1.2...1.2.2.1.1.1.2.2...1.2.2.2.2.2.1.1...1.2.2.1.2.2.2.2
%e A167256 ...2.2.2.2.2.2.2.2...1.1.2.2.2.2.2.2...2.2.2.2.2.2.2.1...1.1.1.1.1.1.1.1
%K A167256 nonn,new
%O A167256 1,2
%A A167256 Ron Hardin (rhhardin(AT)att.net) Oct 31 2009

%I A167255
%S A167255 1,21,441,9157,214689,5850115,158753814,4292655082
%N A167255 Number of ways to partition a n X 7 grid into 7 connected equal-area regions
%e A167255 Some solutions for n=4
%e A167255 ...1.1.1.2.3.3.3...1.2.2.2.3.3.4...1.1.1.1.2.2.3...1.2.2.2.2.3.4
%e A167255 ...1.4.4.2.2.5.3...1.2.5.5.5.3.4...4.4.4.4.5.2.3...1.5.6.6.3.3.4
%e A167255 ...6.6.4.4.2.5.5...1.6.6.6.5.3.4...6.7.7.7.5.2.3...1.5.6.6.7.3.4
%e A167255 ...6.6.7.7.7.7.5...1.6.7.7.7.7.4...6.6.6.7.5.5.3...1.5.5.7.7.7.4
%e A167255 ------
%e A167255 ...1.1.1.1.2.2.3...1.2.2.3.4.4.4...1.2.3.3.3.4.4...1.1.2.2.2.3.3
%e A167255 ...4.4.5.2.2.6.3...1.1.2.3.3.4.5...1.2.2.3.5.4.4...4.1.5.2.6.7.3
%e A167255 ...4.5.5.5.6.6.3...6.1.2.3.7.5.5...1.2.6.6.5.7.7...4.1.5.6.6.7.3
%e A167255 ...4.7.7.7.7.6.3...6.6.6.7.7.7.5...1.6.6.5.5.7.7...4.4.5.5.6.7.7
%e A167255 ------
%e A167255 ...1.1.1.2.3.4.4...1.1.1.1.2.3.3...1.2.2.3.4.5.5...1.1.1.2.2.3.3
%e A167255 ...5.1.2.2.3.6.4...4.4.2.2.2.5.3...1.2.2.3.4.5.5...1.4.2.2.5.5.3
%e A167255 ...5.5.5.2.3.6.4...4.6.6.6.6.5.3...1.1.6.3.4.7.7...6.4.4.4.5.5.3
%e A167255 ...7.7.7.7.3.6.6...4.7.7.7.7.5.5...6.6.6.3.4.7.7...6.6.6.7.7.7.7
%K A167255 nonn,new
%O A167255 1,2
%A A167255 Ron Hardin (rhhardin(AT)att.net) Oct 31 2009

%I A167254
%S A167254 1,13,170,2003,27950,451206,6633399,99697633,1418159011
%N A167254 Number of ways to partition a n X 6 grid into 6 connected equal-area regions
%e A167254 Some solutions for n=4
%e A167254 ...1.1.2.2.2.3...1.1.1.1.2.3...1.2.2.2.2.3...1.1.2.2.2.3...1.1.1.2.2.2
%e A167254 ...1.4.4.2.3.3...4.4.2.2.2.3...1.1.1.3.3.3...1.1.2.4.4.3...1.3.3.3.3.2
%e A167254 ...1.4.4.5.5.3...5.4.4.6.6.3...4.5.5.5.6.6...5.6.6.6.4.3...4.4.5.5.6.6
%e A167254 ...6.6.6.6.5.5...5.5.5.6.6.3...4.4.4.5.6.6...5.5.5.6.4.3...4.4.5.5.6.6
%e A167254 ------
%e A167254 ...1.1.1.2.3.3...1.2.3.3.3.3...1.1.2.2.2.2...1.2.3.4.4.5...1.1.1.1.2.2
%e A167254 ...1.2.2.2.3.3...1.2.2.2.4.4...3.1.4.5.5.5...1.2.3.4.5.5...3.3.3.3.2.4
%e A167254 ...4.4.5.5.5.5...1.5.5.6.4.4...3.1.4.4.6.5...1.2.3.4.6.5...5.6.6.6.2.4
%e A167254 ...4.4.6.6.6.6...1.5.5.6.6.6...3.3.4.6.6.6...1.2.3.6.6.6...5.5.5.6.4.4
%e A167254 ------
%e A167254 ...1.1.2.2.2.3...1.1.2.3.3.4...1.2.2.3.3.3...1.1.2.3.3.3...1.1.2.2.2.3
%e A167254 ...1.4.2.5.5.3...1.2.2.2.3.4...1.2.2.3.4.5...1.4.2.5.5.3...1.1.2.3.3.3
%e A167254 ...1.4.5.5.6.3...1.5.5.6.3.4...1.6.4.4.4.5...1.4.2.5.6.6...4.4.4.5.5.5
%e A167254 ...4.4.6.6.6.3...5.5.6.6.6.4...1.6.6.6.5.5...4.4.2.5.6.6...4.6.6.6.6.5
%K A167254 nonn,new
%O A167254 1,2
%A A167254 Ron Hardin (rhhardin(AT)att.net) Oct 31 2009

%I A167253
%S A167253 1,9,132,1787,22889,264500
%N A167253 Number of ways to partition a n X 6 grid into 3 connected equal-area regions
%e A167253 Some solutions for n=4
%e A167253 ...1.1.1.1.1.2...1.1.1.1.1.1...1.1.1.1.2.2...1.1.1.2.2.2...1.1.2.2.2.2
%e A167253 ...1.1.3.2.2.2...2.2.2.2.3.1...1.1.1.2.2.2...1.3.3.2.2.2...1.2.2.2.3.2
%e A167253 ...3.1.3.2.2.2...2.2.2.2.3.1...3.3.1.2.2.2...1.1.3.3.2.2...1.3.3.3.3.3
%e A167253 ...3.3.3.3.3.2...3.3.3.3.3.3...3.3.3.3.3.3...1.1.3.3.3.3...1.1.1.1.3.3
%e A167253 ------
%e A167253 ...1.1.1.1.2.3...1.1.1.2.3.3...1.2.2.2.2.2...1.1.2.3.3.3...1.1.1.1.1.1
%e A167253 ...1.2.1.2.2.3...1.2.2.2.3.3...1.2.1.2.3.2...1.1.2.2.3.3...2.2.2.2.1.1
%e A167253 ...1.2.2.2.3.3...1.2.2.2.3.3...1.1.1.1.3.3...1.1.2.2.2.3...2.3.3.3.3.3
%e A167253 ...1.2.3.3.3.3...1.1.1.2.3.3...1.3.3.3.3.3...1.1.2.2.3.3...2.2.2.3.3.3
%e A167253 ------
%e A167253 ...1.1.1.1.1.1...1.1.2.2.2.2...1.2.2.2.3.3...1.1.1.1.1.1...1.1.1.1.1.1
%e A167253 ...1.2.2.2.3.1...1.3.3.3.3.2...1.1.1.2.3.3...2.1.2.1.3.3...2.2.2.2.2.1
%e A167253 ...2.2.3.2.3.3...1.3.1.3.3.2...1.2.2.2.2.3...2.2.2.2.2.3...2.2.3.3.3.1
%e A167253 ...2.2.3.3.3.3...1.1.1.3.2.2...1.1.1.3.3.3...2.3.3.3.3.3...2.3.3.3.3.3
%K A167253 nonn,new
%O A167253 1,2
%A A167253 Ron Hardin (rhhardin(AT)att.net) Oct 31 2009

%I A167252
%S A167252 1,6,85,856,8171,80518
%N A167252 Number of ways to partition a n X 6 grid into 2 connected equal-area regions
%e A167252 Some solutions for n=4
%e A167252 ...1.1.1.1.1.1...1.1.1.1.1.1...1.1.1.1.1.2...1.1.1.1.1.1...1.1.1.1.1.1
%e A167252 ...1.2.1.2.2.2...1.2.2.2.1.2...1.2.2.1.1.2...1.1.1.2.1.2...2.1.1.1.1.2
%e A167252 ...1.2.1.1.1.2...1.2.2.2.2.2...1.2.2.1.1.2...2.1.2.2.1.2...2.2.2.1.1.2
%e A167252 ...2.2.2.2.2.2...1.1.1.2.2.2...1.2.2.2.2.2...2.2.2.2.2.2...2.2.2.2.2.2
%e A167252 ------
%e A167252 ...1.1.1.1.1.1...1.1.1.1.1.1...1.1.1.2.2.2...1.2.2.2.2.2...1.1.1.1.1.1
%e A167252 ...1.1.2.2.2.1...1.1.1.2.1.1...1.2.2.2.2.2...1.1.1.2.1.2...1.2.1.2.2.1
%e A167252 ...1.2.2.2.1.1...1.2.2.2.2.2...1.2.2.1.1.2...1.2.2.2.1.2...1.2.2.2.2.2
%e A167252 ...2.2.2.2.2.2...2.2.2.2.2.2...1.1.1.1.1.2...1.1.1.1.1.2...1.1.2.2.2.2
%e A167252 ------
%e A167252 ...1.1.1.1.1.2...1.1.1.1.1.1...1.1.1.1.1.1...1.1.1.1.1.1...1.1.1.1.1.2
%e A167252 ...1.1.2.1.2.2...1.1.2.1.2.1...1.1.1.1.2.1...2.1.2.1.1.1...1.1.1.1.2.2
%e A167252 ...1.2.2.2.2.2...1.2.2.2.2.1...1.2.2.2.2.2...2.1.2.1.2.2...1.2.1.1.2.2
%e A167252 ...1.1.1.2.2.2...2.2.2.2.2.2...2.2.2.2.2.2...2.2.2.2.2.2...2.2.2.2.2.2
%K A167252 nonn,new
%O A167252 1,2
%A A167252 Ron Hardin (rhhardin(AT)att.net) Oct 31 2009

%I A167251
%S A167251 1,8,62,454,4006,33344,270827,2152050,15661597,113764225,757566033
%N A167251 Number of ways to partition a n X 5 grid into 5 connected equal-area regions
%e A167251 Some solutions for n=3
%e A167251 ...1.1.2.2.2...1.1.1.2.3...1.2.3.4.4...1.1.2.2.3...1.1.1.2.3...1.2.2.2.3
%e A167251 ...3.1.4.5.5...4.5.5.2.3...1.2.3.5.4...1.4.2.3.3...4.4.5.2.3...1.4.4.4.3
%e A167251 ...3.3.4.4.5...4.4.5.2.3...1.2.3.5.5...4.4.5.5.5...4.5.5.2.3...1.5.5.5.3
%e A167251 ------
%e A167251 ...1.1.2.2.2...1.1.1.2.2...1.1.2.2.3...1.2.2.3.3...1.1.2.3.3...1.2.3.3.4
%e A167251 ...1.3.4.4.4...3.4.4.5.2...4.1.2.3.3...1.1.2.3.4...4.1.2.3.5...1.2.3.5.4
%e A167251 ...3.3.5.5.5...3.3.4.5.5...4.4.5.5.5...5.5.5.4.4...4.4.2.5.5...1.2.5.5.4
%e A167251 ------
%e A167251 ...1.2.2.3.3...1.2.3.4.5...1.2.2.2.3...1.2.2.3.3...1.2.3.3.3...1.2.2.3.4
%e A167251 ...1.2.4.5.3...1.2.3.4.5...1.1.4.4.3...1.2.4.3.5...1.2.4.4.5...1.2.3.3.4
%e A167251 ...1.4.4.5.5...1.2.3.4.5...5.5.5.4.3...1.4.4.5.5...1.2.4.5.5...1.5.5.5.4
%e A167251 ------
%e A167251 ...1.1.2.3.3...1.1.2.2.2...1.1.2.3.4...1.1.2.2.3...1.1.2.2.2...1.1.2.3.3
%e A167251 ...1.2.2.4.3...1.3.4.5.5...1.5.2.3.4...4.1.2.5.3...3.1.4.4.4...1.4.2.2.3
%e A167251 ...5.5.5.4.4...3.3.4.4.5...5.5.2.3.4...4.4.5.5.3...3.3.5.5.5...4.4.5.5.5
%K A167251 nonn,new
%O A167251 1,2
%A A167251 Ron Hardin (rhhardin(AT)att.net) Oct 31 2009

%I A167250
%S A167250 1,36,939,40899,890989,25878086,543568577
%N A167250 Number of ways to partition a 2*n X 4 grid into 8 connected equal-area regions
%e A167250 Some solutions for n=3
%e A167250 ...1.2.3.3...1.1.2.3...1.2.2.3...1.2.2.2...1.2.3.3...1.1.2.2...1.1.2.2
%e A167250 ...1.2.4.3...4.1.2.3...1.1.2.3...1.3.3.4...1.2.4.3...1.3.2.4...3.1.2.4
%e A167250 ...1.2.4.4...4.5.2.3...4.5.5.3...1.3.4.4...1.2.4.4...3.3.4.4...3.3.4.4
%e A167250 ...5.5.5.6...4.5.6.7...4.5.6.6...5.6.6.7...5.6.6.7...5.6.7.7...5.5.5.6
%e A167250 ...7.8.8.6...8.5.6.7...4.7.6.8...5.6.8.7...5.6.8.7...5.6.8.7...7.7.7.6
%e A167250 ...7.7.8.6...8.8.6.7...7.7.8.8...5.8.8.7...5.8.8.7...5.6.8.8...8.8.8.6
%e A167250 ------
%e A167250 ...1.1.2.3...1.2.2.3...1.2.2.3...1.2.3.3...1.2.3.3...1.1.2.2...1.2.3.4
%e A167250 ...1.2.2.3...1.4.2.3...1.1.2.3...1.2.2.3...1.2.4.3...3.1.2.4...1.2.3.4
%e A167250 ...4.4.4.3...1.4.4.3...4.4.4.3...1.4.4.4...1.2.4.4...3.5.4.4...1.2.3.4
%e A167250 ...5.6.6.7...5.6.6.6...5.5.5.6...5.5.5.6...5.6.7.7...3.5.5.6...5.5.6.6
%e A167250 ...5.5.6.7...5.7.8.8...7.7.6.6...7.7.6.6...5.6.6.7...7.8.8.6...5.7.8.6
%e A167250 ...8.8.8.7...5.7.7.8...7.8.8.8...7.8.8.8...5.8.8.8...7.7.8.6...7.7.8.8
%K A167250 nonn,new
%O A167250 1,2
%A A167250 Ron Hardin (rhhardin(AT)att.net) Oct 31 2009

%I A167249
%S A167249 11,2003,244252,22351172,1403637121
%N A167249 Number of ways to partition a 3*n X 4 grid into 6 connected equal-area regions
%e A167249 Some solutions for n=3
%e A167249 ...1.1.1.2...1.1.1.2...1.1.1.2...1.1.1.2...1.1.1.2...1.1.1.2...1.1.1.2
%e A167249 ...1.1.2.2...1.1.2.2...1.1.2.2...1.1.2.2...1.1.2.2...1.1.2.2...1.1.2.2
%e A167249 ...1.3.2.2...1.3.2.2...1.3.2.2...1.3.2.2...1.3.2.2...1.3.2.2...1.3.2.2
%e A167249 ...4.3.3.2...3.3.3.2...3.3.3.2...3.3.3.2...3.3.3.2...3.3.3.2...3.3.3.2
%e A167249 ...4.3.3.5...4.3.3.5...4.3.5.5...3.3.4.4...3.3.4.4...4.3.3.5...3.3.4.4
%e A167249 ...4.6.3.5...4.6.6.5...4.3.5.5...4.4.4.4...5.4.4.4...4.6.5.5...5.5.5.4
%e A167249 ...4.6.5.5...4.4.6.5...4.6.6.5...5.6.6.6...5.6.6.4...4.6.6.5...5.6.6.4
%e A167249 ...4.6.5.5...4.6.6.5...4.6.6.5...5.6.6.6...5.6.6.6...4.6.6.5...5.6.4.4
%e A167249 ...4.6.6.6...4.6.5.5...4.4.6.6...5.5.5.5...5.5.5.6...4.4.6.5...5.6.6.6
%K A167249 nonn,new
%O A167249 1,1
%A A167249 Ron Hardin (rhhardin(AT)att.net) Oct 31 2009

%I A167248
%S A167248 1,5,23,117,501,2369,9525,39731,145415,554487,1975561,7301317,25334269
%N A167248 Number of ways to partition a n X 4 grid into 4 connected equal-area regions
%e A167248 All solutions for n=3
%e A167248 ...1.1.2.3...1.1.2.2...1.1.2.2...1.1.2.3...1.1.2.2...1.1.2.2...1.1.1.2
%e A167248 ...1.2.2.3...1.3.2.4...1.3.4.2...1.4.2.3...3.1.2.4...3.1.4.2...3.3.2.2
%e A167248 ...4.4.4.3...3.3.4.4...3.3.4.4...4.4.2.3...3.3.4.4...3.3.4.4...3.4.4.4
%e A167248 ------
%e A167248 ...1.1.1.2...1.1.1.2...1.1.1.2...1.1.2.3...1.2.2.2...1.2.2.3...1.2.2.3
%e A167248 ...3.3.4.2...3.3.3.2...3.4.4.2...4.1.2.3...1.1.3.3...1.1.2.3...1.2.3.3
%e A167248 ...3.4.4.2...4.4.4.2...3.3.4.2...4.4.2.3...4.4.4.3...4.4.4.3...1.4.4.4
%e A167248 ------
%e A167248 ...1.2.2.3...1.2.3.3...1.2.3.3...1.2.3.3...1.2.3.4...1.2.2.2...1.2.2.2
%e A167248 ...1.2.4.3...1.2.2.3...1.2.3.4...1.2.4.3...1.2.3.4...1.3.3.4...1.3.3.3
%e A167248 ...1.4.4.3...1.4.4.4...1.2.4.4...1.2.4.4...1.2.3.4...1.3.4.4...1.4.4.4
%e A167248 ------
%e A167248 ...1.2.2.2...1.2.2.3
%e A167248 ...1.3.4.4...1.4.2.3
%e A167248 ...1.3.3.4...1.4.4.3
%K A167248 nonn,new
%O A167248 1,2
%A A167248 Ron Hardin (rhhardin(AT)att.net) Oct 31 2009

%I A167247
%S A167247 1,4,19,70,245,856,2967,10164,34463,115904,387379,1288574,4270853,
%T A167247 14116936,46567963,153385198
%N A167247 Number of ways to partition a n X 4 grid into 2 connected equal-area regions
%e A167247 All solutions for n=3
%e A167247 ...1.1.1.1...1.1.1.1...1.1.1.1...1.1.1.1...1.1.1.1...1.1.1.1...1.1.1.1
%e A167247 ...1.1.2.2...1.2.1.2...1.2.2.1...1.2.2.2...2.1.1.2...2.1.2.1...2.2.1.1
%e A167247 ...2.2.2.2...2.2.2.2...2.2.2.2...1.2.2.2...2.2.2.2...2.2.2.2...2.2.2.2
%e A167247 ------
%e A167247 ...1.1.1.1...1.1.1.2...1.1.1.2...1.1.1.2...1.1.1.2...1.1.2.2...1.1.2.2
%e A167247 ...2.2.2.1...1.1.1.2...1.1.2.2...1.2.1.2...1.2.2.2...1.1.1.2...1.1.2.2
%e A167247 ...2.2.2.1...2.2.2.2...1.2.2.2...1.2.2.2...1.1.2.2...1.2.2.2...1.1.2.2
%e A167247 ------
%e A167247 ...1.1.2.2...1.2.2.2...1.2.2.2...1.2.2.2...1.2.2.2
%e A167247 ...1.2.2.2...1.1.1.2...1.1.2.2...1.2.1.2...1.2.2.2
%e A167247 ...1.1.1.2...1.1.2.2...1.1.1.2...1.1.1.2...1.1.1.1
%K A167247 nonn,new
%O A167247 1,2
%A A167247 Ron Hardin (rhhardin(AT)att.net) Oct 31 2009

%I A167246
%S A167246 1,41,3127,44855,1082911,29384641,331247456
%N A167246 Number of ways to partition a 3*n X 3 grid into 9 connected equal-area regions
%e A167246 Some solutions for n=3
%e A167246 ...1.2.2...1.2.2...1.2.3...1.1.2...1.1.2...1.1.1...1.1.1...1.1.2...1.1.2
%e A167246 ...1.3.2...1.1.2...1.2.3...3.1.2...1.2.2...2.2.2...2.2.2...1.3.2...1.3.2
%e A167246 ...1.3.3...3.3.4...1.2.3...3.4.2...3.4.5...3.3.3...3.3.4...3.3.2...3.3.2
%e A167246 ...4.5.6...3.4.4...4.4.4...3.4.4...3.4.5...4.5.5...3.4.4...4.4.5...4.4.4
%e A167246 ...4.5.6...5.5.5...5.6.6...5.5.5...3.4.5...4.4.5...5.6.6...4.5.5...5.5.5
%e A167246 ...4.5.6...6.6.6...5.7.6...6.7.7...6.6.6...6.7.7...5.6.7...6.7.7...6.6.6
%e A167246 ...7.8.8...7.8.8...5.7.7...6.6.7...7.7.8...6.7.8...5.7.7...6.8.7...7.8.8
%e A167246 ...7.8.9...7.8.9...8.8.8...8.9.9...7.8.8...6.9.8...8.8.8...6.8.8...7.9.8
%e A167246 ...7.9.9...7.9.9...9.9.9...8.8.9...9.9.9...9.9.8...9.9.9...9.9.9...7.9.9
%K A167246 nonn,new
%O A167246 1,2
%A A167246 Ron Hardin (rhhardin(AT)att.net) Oct 31 2009

%I A167245
%S A167245 1,11,170,997,7670,62609,296063,1685893,9684421,41633825
%N A167245 Number of ways to partition a 2*n X 3 grid into 6 connected equal-area regions
%e A167245 Some solutions for n=4
%e A167245 ...1.1.2...1.1.1...1.1.2...1.1.2...1.1.1...1.2.2...1.2.2...1.2.2...1.1.1
%e A167245 ...1.2.2...2.1.3...3.1.2...1.2.2...2.3.1...1.2.2...1.1.2...1.2.2...2.1.3
%e A167245 ...1.3.2...2.3.3...3.1.2...1.2.3...2.3.3...1.3.3...1.3.2...1.3.3...2.3.3
%e A167245 ...3.3.4...2.2.3...3.4.2...4.3.3...2.3.4...1.3.3...3.3.4...1.3.3...2.4.3
%e A167245 ...3.4.4...4.4.4...3.4.4...4.4.3...2.4.4...4.4.4...5.3.4...4.4.4...2.4.4
%e A167245 ...5.4.6...5.4.6...5.5.4...5.4.6...5.4.6...4.5.5...5.6.4...4.5.5...5.4.6
%e A167245 ...5.5.6...5.5.6...6.5.5...5.6.6...5.5.6...6.5.5...5.6.4...6.6.5...5.5.6
%e A167245 ...5.6.6...5.6.6...6.6.6...5.5.6...5.6.6...6.6.6...5.6.6...6.6.5...5.6.6
%K A167245 nonn,new
%O A167245 1,2
%A A167245 Ron Hardin (rhhardin(AT)att.net) Oct 31 2009

%I A167244
%S A167244 23,1038,25663,508866,9030533
%N A167244 Number of ways to partition a 4*n X 3 grid into 4 connected equal-area regions
%e A167244 Some solutions for n=3
%e A167244 ...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1
%e A167244 ...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1
%e A167244 ...1.1.2...1.1.2...1.1.2...1.1.2...1.1.2...1.1.2...1.1.2...1.1.2...1.1.2
%e A167244 ...1.2.2...1.2.2...1.2.2...1.2.2...1.2.2...1.2.2...1.2.2...1.2.2...1.2.2
%e A167244 ...3.2.2...3.2.4...2.2.2...2.2.2...2.2.2...2.2.2...2.2.2...2.2.2...2.2.2
%e A167244 ...3.2.2...3.2.4...3.2.2...2.2.3...3.2.2...2.2.2...3.2.2...2.3.3...2.2.2
%e A167244 ...3.4.2...3.2.4...3.3.2...4.2.3...3.3.2...3.3.3...3.3.2...2.4.3...3.3.3
%e A167244 ...3.4.2...3.2.4...3.4.4...4.4.3...3.4.4...4.4.3...4.3.3...2.4.3...4.4.3
%e A167244 ...3.4.4...3.2.4...3.4.4...4.3.3...3.3.4...4.4.3...4.3.3...4.4.3...4.3.3
%e A167244 ...3.4.4...3.2.4...3.3.4...4.4.3...3.4.4...4.4.3...4.4.3...4.4.3...4.3.3
%e A167244 ...3.4.4...3.4.4...3.4.4...4.4.3...3.4.4...4.3.3...4.4.3...4.3.3...4.3.4
%e A167244 ...3.3.4...3.3.4...3.4.4...4.3.3...3.4.4...4.4.3...4.4.4...4.4.3...4.4.4
%K A167244 nonn,new
%O A167244 1,1
%A A167244 Ron Hardin (rhhardin(AT)att.net) Oct 31 2009

%I A167243
%S A167243 1,3,10,23,56,132,259,546,1095,2043,3908,7379,13208,24194,43819,76790,
%T A167243 136489,241311,416152,726073,1261696,2153026,3706393,6364842,10775173,
%U A167243 18374181
%N A167243 Number of ways to partition a n X 3 grid into 3 connected equal-area regions
%e A167243 All solutions for n=4
%e A167243 ...1.1.2...1.1.2...1.1.2...1.1.2...1.1.2...1.1.2...1.1.1...1.1.1...1.1.1
%e A167243 ...1.2.2...1.2.2...1.1.2...1.1.2...1.3.2...3.1.2...1.2.2...1.2.2...1.2.2
%e A167243 ...1.2.3...1.3.2...3.2.2...3.3.2...1.3.2...3.1.2...2.2.3...3.2.2...3.3.2
%e A167243 ...3.3.3...3.3.3...3.3.3...3.3.2...3.3.2...3.3.2...3.3.3...3.3.3...3.3.2
%e A167243 ------
%e A167243 ...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1...1.2.2...1.2.2
%e A167243 ...1.2.3...2.2.1...2.2.1...2.2.1...2.1.3...2.1.3...2.3.1...1.2.2...1.2.2
%e A167243 ...2.2.3...2.2.3...2.3.3...3.2.2...2.2.3...2.3.3...2.3.3...1.1.3...1.3.3
%e A167243 ...2.3.3...3.3.3...2.3.3...3.3.3...2.3.3...2.2.3...2.2.3...3.3.3...1.3.3
%e A167243 ------
%e A167243 ...1.2.2...1.2.2...1.2.2...1.2.2...1.2.3
%e A167243 ...1.2.3...1.1.2...1.1.2...1.3.2...1.2.3
%e A167243 ...1.2.3...1.3.2...3.1.2...1.3.2...1.2.3
%e A167243 ...1.3.3...3.3.3...3.3.3...1.3.3...1.2.3
%K A167243 nonn,new
%O A167243 1,2
%A A167243 Ron Hardin (rhhardin(AT)att.net) Oct 31 2009

%I A167242
%S A167242 3,19,85,355,1435,5717,22645,89521,353735,1397863,5525341,21846421,
%T A167242 86403027,341822335,1352660761,5354124895,21197945407,83945924393,
%U A167242 332507403625,1317329758675
%N A167242 Number of ways to partition a 2*n X 3 grid into 2 connected equal-area regions
%e A167242 Some solutions for n=4
%e A167242 ...1.1.1...1.1.1...1.1.2...1.1.2...1.1.2...1.1.1...1.1.1...1.1.1...1.1.1
%e A167242 ...1.1.1...1.1.2...1.2.2...1.1.2...1.2.2...2.2.1...1.1.1...2.1.1...1.1.1
%e A167242 ...2.2.1...1.2.2...1.1.2...1.2.2...1.2.2...2.2.1...2.1.1...2.2.1...2.1.1
%e A167242 ...2.1.1...1.2.2...1.2.2...1.2.2...1.1.2...2.2.1...2.2.1...2.1.1...2.2.1
%e A167242 ...2.2.1...1.2.2...1.1.2...1.2.2...1.1.2...2.1.1...2.2.1...2.2.1...2.2.1
%e A167242 ...2.2.1...1.1.2...1.1.2...1.2.2...1.1.2...2.1.1...2.1.1...2.1.1...2.2.1
%e A167242 ...2.2.1...1.2.2...1.2.2...1.1.2...1.1.2...2.1.1...2.2.2...2.1.2...2.2.1
%e A167242 ...2.2.2...1.2.2...1.2.2...1.1.2...2.2.2...2.2.2...2.2.2...2.2.2...2.2.2
%K A167242 nonn,new
%O A167242 1,1
%A A167242 Ron Hardin (rhhardin(AT)att.net) Oct 31 2009

%I A167241
%S A167241 1,34,153,1156,4361,16182,44561,115784
%N A167241 Number of ways to partition a 4*n X 2 grid into 8 connected equal-area regions
%e A167241 Some solutions for n=4
%e A167241 ...1.1...1.1...1.1...1.1...1.1...1.1...1.1...1.2...1.1...1.1...1.1...1.1...1.1
%e A167241 ...2.1...2.1...1.2...1.1...2.1...1.2...1.2...1.2...1.2...1.1...1.2...1.2...2.1
%e A167241 ...2.1...2.1...1.2...2.2...2.1...1.2...1.2...1.2...1.2...2.2...1.2...1.2...2.1
%e A167241 ...2.2...2.2...2.2...3.2...2.3...2.2...3.2...1.2...2.2...2.3...2.2...3.2...2.3
%e A167241 ...3.3...3.3...3.3...3.2...2.3...3.3...3.2...3.4...3.3...2.3...3.3...3.2...2.3
%e A167241 ...3.4...3.3...3.4...3.3...3.3...4.3...3.3...3.4...3.4...3.3...4.3...3.3...3.3
%e A167241 ...3.4...4.4...3.4...4.4...4.4...4.3...4.4...3.4...3.4...4.4...4.3...4.4...4.4
%e A167241 ...5.4...5.4...4.4...4.5...4.4...4.4...5.4...3.4...5.4...4.5...4.5...4.4...4.5
%e A167241 ...5.4...5.4...5.5...4.5...5.5...5.5...5.4...5.6...5.4...4.5...4.5...5.5...4.5
%e A167241 ...5.5...5.5...6.5...5.5...5.6...5.5...5.6...5.6...5.5...5.5...6.5...6.5...5.5
%e A167241 ...6.6...6.6...6.5...6.6...5.6...6.7...5.6...5.6...6.6...6.6...6.5...6.5...6.6
%e A167241 ...6.7...6.6...6.7...6.7...6.6...6.7...7.6...5.6...6.6...6.7...6.7...6.7...6.6
%e A167241 ...6.7...7.7...6.7...6.7...7.7...6.7...7.6...7.7...7.7...6.7...6.7...6.7...7.7
%e A167241 ...8.7...7.8...8.7...8.7...7.8...6.7...7.7...7.7...7.7...8.7...8.7...7.7...7.8
%e A167241 ...8.7...7.8...8.7...8.7...7.8...8.8...8.8...8.8...8.8...8.7...8.7...8.8...7.8
%e A167241 ...8.8...8.8...8.8...8.8...8.8...8.8...8.8...8.8...8.8...8.8...8.8...8.8...8.8
%K A167241 nonn,new
%O A167241 1,2
%A A167241 Ron Hardin (rhhardin(AT)att.net) Oct 31 2009

%I A167240
%S A167240 1,13,41,169,441,1109,2289,4497,7953,13533,21593,33465,49673,72101,
%T A167240 101473,140321,189601
%N A167240 Number of ways to partition a 3*n X 2 grid into 6 connected equal-area regions
%e A167240 Some solutions for n=4
%e A167240 ...1.1...1.2...1.1...1.1...1.1...1.1...1.2...1.1...1.1...1.1...1.1...1.1...1.1
%e A167240 ...1.2...1.2...1.2...1.2...1.2...1.2...1.2...1.1...1.2...1.1...1.1...2.1...2.1
%e A167240 ...1.2...1.2...1.2...1.2...1.2...1.2...1.2...2.2...1.2...2.2...2.2...2.1...2.1
%e A167240 ...3.2...1.2...2.2...2.2...3.2...2.2...1.2...3.2...2.2...2.3...2.3...2.3...2.2
%e A167240 ...3.2...3.3...3.3...3.3...3.2...3.3...3.4...3.2...3.3...2.3...2.3...2.3...3.3
%e A167240 ...3.3...3.3...3.4...4.3...3.4...3.3...3.4...3.4...3.3...3.3...3.3...3.3...4.3
%e A167240 ...4.4...4.4...3.4...4.3...3.4...4.4...3.4...3.4...4.4...4.4...4.4...4.4...4.3
%e A167240 ...5.4...5.4...5.4...4.4...4.4...4.4...3.4...4.4...4.5...4.4...4.4...4.4...4.4
%e A167240 ...5.4...5.4...5.4...5.6...5.5...5.5...5.5...5.5...4.5...5.5...5.6...5.5...5.5
%e A167240 ...5.6...5.5...5.6...5.6...5.6...5.6...6.5...6.5...6.5...5.5...5.6...5.5...5.5
%e A167240 ...5.6...6.6...5.6...5.6...5.6...5.6...6.5...6.5...6.5...6.6...5.6...6.6...6.6
%e A167240 ...6.6...6.6...6.6...5.6...6.6...6.6...6.6...6.6...6.6...6.6...5.6...6.6...6.6
%K A167240 nonn,new
%O A167240 1,2
%A A167240 Ron Hardin (rhhardin(AT)att.net) Oct 31 2009

%I A167239
%S A167239 8,64,288,880,2120,4368,8064,13728,21960,33440,48928,69264
%N A167239 Number of ways to partition a 5*n X 2 grid into 5 connected equal-area regions
%e A167239 Some solutions for n=4
%e A167239 ...1.1...1.1...1.1...1.1...1.1...1.1...1.1...1.1...1.1...1.1...1.1...1.1...1.1
%e A167239 ...1.1...1.2...1.1...1.1...1.1...2.1...1.1...2.1...1.1...1.2...1.1...1.1...1.1
%e A167239 ...1.1...1.2...2.1...1.2...2.1...2.1...1.2...2.1...1.1...1.2...1.1...1.2...1.1
%e A167239 ...2.1...1.2...2.1...1.2...2.1...2.1...1.2...2.1...1.2...1.2...2.1...1.2...1.2
%e A167239 ...2.1...1.2...2.1...1.2...2.1...2.1...1.2...2.1...1.2...1.2...2.1...1.2...1.2
%e A167239 ...2.2...1.2...2.1...1.2...2.1...2.1...1.2...2.1...2.2...1.2...2.2...1.2...2.2
%e A167239 ...2.2...1.2...2.2...3.2...2.2...2.1...2.2...2.1...2.2...1.2...2.2...2.2...2.2
%e A167239 ...2.2...3.2...2.2...3.2...2.2...2.2...2.2...2.3...3.2...2.2...2.3...2.2...3.2
%e A167239 ...3.4...3.2...3.3...3.2...3.3...3.3...3.3...2.3...3.2...3.3...2.3...3.3...3.2
%e A167239 ...3.4...3.3...3.3...3.2...3.3...3.3...3.3...3.3...3.3...3.3...3.3...3.3...3.3
%e A167239 ...3.4...3.3...3.3...3.3...3.3...3.3...3.3...3.3...3.3...4.3...3.3...3.3...3.3
%e A167239 ...3.4...3.4...4.3...3.3...3.3...3.3...4.3...3.4...4.3...4.3...3.3...3.3...3.3
%e A167239 ...3.4...3.4...4.3...4.4...4.4...4.4...4.3...3.4...4.3...4.3...4.4...4.4...4.5
%e A167239 ...3.4...4.4...4.5...4.4...4.5...4.4...4.4...4.4...4.4...4.3...4.4...4.4...4.5
%e A167239 ...3.4...5.4...4.5...4.5...4.5...4.4...5.4...4.4...4.5...4.4...4.4...4.4...4.5
%e A167239 ...3.4...5.4...4.5...4.5...4.5...5.4...5.4...4.5...4.5...4.5...5.4...4.5...4.5
%e A167239 ...5.5...5.4...4.5...4.5...4.5...5.4...5.4...4.5...4.5...4.5...5.4...4.5...4.5
%e A167239 ...5.5...5.4...4.5...4.5...4.5...5.5...5.4...5.5...4.5...5.5...5.5...5.5...4.5
%e A167239 ...5.5...5.5...4.5...5.5...4.5...5.5...5.5...5.5...5.5...5.5...5.5...5.5...4.5
%e A167239 ...5.5...5.5...5.5...5.5...5.5...5.5...5.5...5.5...5.5...5.5...5.5...5.5...4.5
%K A167239 nonn,new
%O A167239 1,1
%A A167239 Ron Hardin (rhhardin(AT)att.net) Oct 31 2009

%I A167238
%S A167238 1,5,11,25,45,77,119,177,249,341,451,585,741,925,1135,1377,1649,1957,
%T A167238 2299,2681,3101,3565,4071,4625,5225,5877,6579,7337,8149,9021,9951,10945,
%U A167238 12001,13125,14315,15577
%N A167238 Number of ways to partition a 2*n X 2 grid into 4 connected equal-area regions
%F A167238 Empirical: a(n)=3*a(n-1)-2*a(n-2)-2*a(n-3)+3*a(n-4)-a(n-5)
%e A167238 All solutions for n=3
%e A167238 ...1.1...1.1...1.1...1.1...1.1...1.1...1.1...1.1...1.2...1.2...1.2
%e A167238 ...1.2...1.2...1.2...1.2...2.1...2.1...2.1...2.1...1.2...1.2...1.2
%e A167238 ...2.2...2.2...2.2...3.2...2.2...2.2...2.2...2.3...1.2...1.2...1.2
%e A167238 ...3.3...3.3...3.4...3.2...3.3...3.3...3.4...2.3...3.3...3.3...3.4
%e A167238 ...3.4...4.3...3.4...3.4...3.4...4.3...3.4...4.3...3.4...4.3...3.4
%e A167238 ...4.4...4.4...3.4...4.4...4.4...4.4...3.4...4.4...4.4...4.4...3.4
%K A167238 nonn,new
%O A167238 1,2
%A A167238 Ron Hardin (rhhardin(AT)att.net) Oct 31 2009

%I A080092
%S A080092 2,2,3,2,3,5,2,3,7,2,3,5,2,3,11,2,3,5,7,13,2,3,2,3,5,17,2,3,7,19,2,3,5,11,
%T A080092 2,3,23,2,3,5,7,13,2,3,2,3,5,29,2,3,7,11,31,2,3,5,17,2,3,2,3,5,7,13,19,
%U A080092 37,2,3,2,3,5,11,41,2,3,7,43,2,3,5,23,2,3,47,2,3,5,7,13,17,2,3
%N A080092 Irregular triangle read by rows, giving prime sequences (p-1|2n) appearing in the n-th von Staudt-Clausen sum.
%C A080092 Comments from Gary W. Adamson & Mats O. Granvik (qntmpkt(AT)yahoo.com), Aug 09 2008 (Start) The Von Staudt-Clausen theorem has two parts: generating denominators of the B_2n and the actual values. Both operations can be demonstrated in triangles A143343 and A080092 by following the procedures outlined in [Wikipedia - Bernoulli numbers] and summarized in A143343.
%C A080092 A143345 = number of terms in each row of A080092 (1, 2, 3, 3, 3, 3, 5, 2,...)
%C A080092 The same terms in A143343 may be extracted from triangle A138239.
%C A080092 Extract primes from even numbered rows of triangle A143343 but also include "2" as row 1. The rows are thus 1, 2, 4, 6...; generating denominators of B_1, B_2, B_4,...as well as B_1, B_2, B_4,...; as two parts of the Von Staudt-Clausen theorem.
%C A080092 The denominator of B_12 = 2730 = (2*3*5*7*13) = A027642(12) and A002445(6).
%C A080092 For example, B_12 = -691/2730 = (1 - 1/2 - 1/3 - 1/5 - 1/7 - 1/13)
%C A080092 The second operation is the Von Staudt-Clausen representation of Bn, obtained by starting with "1" then subtracting the reciprocals of terms in each row. (Cf. A143343 for a detailed explanation of the operations). (End)
%D A080092 Wikipedia (Bernoulli numbers).
%H A080092 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/vonStaudt-ClausenTheorem.html">von Staudt-Clausen Theorem</a>
%e A080092 First few rows of the triangle are:
%e A080092 2;
%e A080092 2, 3;
%e A080092 2, 3, 5;
%e A080092 2, 3, 7;
%e A080092 2, 3, 5;
%e A080092 2, 3, 11;
%e A080092 2, 3, 5, 7, 13;
%e A080092 2, 3;
%e A080092 ...
%e A080092 Sum for n=1 is 1/2+1/3, so terms are 2, 3. Sum for n=2 is 1/2+1/3+1/5, so terms are 2, 3, 5. Etc.
%Y A080092 Cf. A000146.
%Y A080092 Cf. A000146, A143343, A143345, A138239, A002445, A027642.
%K A080092 nonn,easy,nice,tabf,new
%O A080092 1,1
%A A080092 Eric Weisstein (eric(AT)weisstein.com), Jan 27, 2003
%E A080092 Edited by njas, Nov 01 2009 at the suggestion of R. J. Mathar

%I A156071
%S A156071 3,38,381,3816,38165,381654,3816547,38165472,381654729
%N A156071 Concatenation chain arising in A156069.
%H A156071 Author?, <a href="http://puzzles.blainesville.com/2008/01/how-about-math-puzzle.html#comments">Title</a>
%K A156071 nonn,base,fini,full
%O A156071 1,1
%A A156071 Alexander Povolotsky (apovolot(AT)gmail.com), Sep 25 2009

%I A156069
%S A156069 3,19,127,954,7633,63609,545221,4770684,42406081
%N A156069 n*a(n) gives the following concatenation chain 3,38,381,3816,38165,381654,3816547,38165472,381654729 (cf. A156071).
%H A156069 Author?, <a href="http://puzzles.blainesville.com/2008/01/how-about-math-puzzle.html#comments">Title</a>
%K A156069 nonn,fini,full,base
%O A156069 1,1
%A A156069 Alexander Povolotsky (apovolot(AT)gmail.com), Sep 25 2009

%I A167270
%S A167270 1,2,4,6,10,15,24,37,59,93,149,238,383,616,994,1604,2592
%N A167270 Row sums, triangle A167269
%C A167270 a(n)/a(n-1) tends to phi, 1.6180339...; e.g. a(16)/a(15) = 2592/1604 = 1.6159...
%F A167270 Row sums of triangle A167269
%e A167270 a(4) = 10 = (1 + 4 + 1 + 3 + 1).
%Y A167270 A167269
%K A167270 nonn,new
%O A167270 0,2
%A A167270 Gary W. Adamson & Mats Granvik (qntmpkt(AT)yahoo.com), Oct 31 2009

%I A167269
%S A167269 1,1,1,1,2,1,1,3,1,1,1,4,1,3,1,1,5,1,6,1,1,1,6,1,10,1,4,1,1,7,1,15,1,10,
%T A167269 1,1,1,8,1,21,1,20,1,5,1,1,9,1,28,1,35,1,15,1,1,1,10,1,36,1,56,1,35,1,6,
%U A167269 1,1,11,1,45,1,84,1,70,1,21,1,1,1,12,1,55,1,120,1,126,1,56,1,7,1
%N A167269 Triangle by rows, Pascal's triangle columns interleaved with 1's.
%C A167269 Row sums, A167270: (1, 2, 4, 6, 10, 15, 24, 37,...) tend to phi, 1.618...;
%C A167269 e.g. 2592/1604 = 1.61596...
%F A167269 Given Pascal's triangle columns >0, insert 1's as alternate columns.
%e A167269 First few rows of the triangle =
%e A167269 1;
%e A167269 1, 1;
%e A167269 1, 2, 1;
%e A167269 1, 3, 1, 1;
%e A167269 1, 4, 1, 3, 1;
%e A167269 1, 5, 1, 6, 1, 1;
%e A167269 1, 6, 1, 10, 1, 4, 1;
%e A167269 1, 7, 1, 15, 1, 10, 1, 1;
%e A167269 1, 8, 1, 21, 1, 20, 1, 5, 1;
%e A167269 1, 9, 1, 28, 1, 35, 1, 15, 1, 1;
%e A167269 1, 10, 1, 36, 1, 56, 1, 35, 1, 6, 1;
%e A167269 1, 11, 1, 45, 1, 84, 1, 70, 1, 21, 1, 1;
%e A167269 1, 12, 1, 55, 1, 120, 1, 126, 1, 56, 1, 7, 1;
%e A167269 1, 13, 1, 66, 1, 165, 1, 210, 1, 126, 1, 28, 1, 1;
%e A167269 1, 14, 1, 78, 1, 220, 1, 330, 1, 252, 1, 84, 1, 8, 1;
%e A167269 1, 15, 1, 91, 1, 286, 1, 495, 1, 462, 1, 210, 1, 36, 1, 1;
%e A167269 1, 16, 1, 105, 1, 364, 1, 715, 1, 792, 1, 461, 1, 120, 1, 9, 1;
%e A167269 ...
%Y A167269 A167270
%K A167269 nonn,tabl,new
%O A167269 0,5
%A A167269 Gary W. Adamson & Mats Granvik (qntmpkt(AT)yahoo.com), Oct 31 2009

%I A167267
%S A167267 1,3,2,7,5,4,12,10,8,6,19,16,14,11,9,28,24,21,18,15,13,38,34,30,26,23,
%T A167267 20,17,50,45,41,36,32,29,25,22,63,58,53,48,43,39,35,31,27,78,72,67,61,
%U A167267 56,51,46,42,37,33
%N A167267 Interspersion of the signature sequence of (1+sqrt(5))/2.
%C A167267 Row n is the ordered sequence of numbers k such that A084531(k)=n.
%C A167267 As a sequence, A167267 is a permutation of the positive integers.
%C A167267 Is the difference sequence of column 1 equal to A019446?
%C A167267 Is the difference sequence of row 1 essentially equal to A026351?
%D A167267 Clark Kimberling, "Fractal Sequences and Interspersions," Ars Combinatoria 45 (1997) 157-168.
%e A167267 Northwest corner:
%e A167267 1 3 7 12 19 28 38
%e A167267 2 5 10 16 24 34 45
%e A167267 4 8 14 21 30 41 53
%e A167267 6 11 18 26 36 48 61
%Y A167267 Cf. A084531.
%K A167267 nonn,tabl,new
%O A167267 1,2
%A A167267 Clark Kimberling (ck6(AT)evansville.edu), Oct 31 2009

%I A167266
%S A167266 1827,2187,102510,105210,105264,115672,116725,123354,125248,125433
%N A167266 Vampire numbers permutations of whose digits are other vampire numbers.
%C A167266 Use definition 2 of vampire numbers; i.e., this is a subsequence of A014575.
%e A167266 The vampire number 102510 is included because all of its digits, including the duplicate 0 and 1, can be rearranged to give at least one other vampire number such as 105210.
%Y A167266 Cf. A014575.
%K A167266 base,more,nonn,new
%O A167266 1,1
%A A167266 Rick L. Shepherd (rshepherd2(AT)hotmail.com), Oct 31 2009, Nov 01 2009

%I A167268
%S A167268 2,2,6,2,6,2,10,6,2,10,6,2,14,10,6,2,14,10,6,2,18,14,10,6,2,18,14,10,6,
%T A167268 2,22,18,14,10,6,2,22,18,14,10,6,2,26,22,18,14,10,6,2,26,22,18,14,10,6,
%U A167268 2
%N A167268 Janet's sequence.Terms from blocks s,p,d,f of Janet table of the elements.
%C A167268 Doubled fractal. For Janet form 8*32 ,from right to left, s=8*2=16 p=6*6=36, d=4*10=40, f=2*14=28 terms ;see submitted A166568=16,36,40,28. p (A138469) and f (lanthanoids and actinoids: 57,58,59,60,61,62,63,64,65,66,67,68,69,70,89,90,91,92,93,94,95,96,97,98,99,100,101,102) are the same for Janet and Mendeleyev-Moseley-Seaborg but not at the same places. a(0)=1+1 terms for H and He; a(1)=1+1 for Li and Be; a(2)=6 for B,C,N,O,F,Ne; a(3)=2 for Na,Mg; a(4)=6 for Al,Si,P,S,Cl,Ar; .. . Reference, 2 leaflet 2,with Janet form (5). Extended. See A016825,A102261.
%D A167268 JANET,Charles, CONSIDERATIONS SUR LA STRUCTURE DU NOYAU DE L'ATOME,N 5,Decembre 1929,BEAUVAIS,2+45 pages,4 leaflets.
%K A167268 nonn,uned,new
%O A167268 0,1
%A A167268 Paul Curtz (bpcrtz(AT)free.fr), Oct 31 2009

%I A156056
%S A156056 1,0,1,3,4,8,11,17,22,26,4,4,9,19,26,30,35,49,56,68,12,16,27,33,34,48,
%T A156056 69,85,108,13,115,4,13,39,34,62,75,89,112,128,145,179,182,25,50,86,73,
%U A156056 61,90,130,161,183,226,230,255,18,39,85,108,144,193,195,174,214,267,309
%N A156056 nth triangular number modulo nth prime.
%t A156056 Table[Mod[n(n + 1)/2, Prime[n]], {n, 100}]
%K A156056 nonn,new
%O A156056 1,4
%A A156056 Zak Seidov (zakseidov(AT)yahoo.com), Oct 31 2009

%I A167237
%S A167237 1,2,1,3,2,1,4,5,3,2,6,1,7,4,8,5,3,9,2,10,6,1,11,7,4,12,13,8,5,14,3,15,
%T A167237 9,2,16,10,6,17,1,18,11,7,19,4,20,12,21,13,8,22,5,23,14,3,24,15,9,25,2,
%U A167237 26,16,10,27,6,28,17,1,29,18,11,30,7,31,19,4,32,20,12
%N A167237 Lower trim of the Wythoff fractal sequence, A003603.
%C A167237 A fractal sequence: if you delete the first occurrence of each positive
%C A167237 integer, the remaining sequence is the original. This procedure is called
%C A167237 upper trimming, in contrast to lower trimming, which consists of
%C A167237 subtracting 1 from each term of the original fractal sequence and then
%C A167237 deleting all 0s. In general, the lower trim of a fractal sequence is a
%C A167237 fractal sequence; in particular, the lower trim of A003603 is A167237.
%D A167237 Clark Kimberling, "Fractal Sequences and Interspersions," Ars Combinatoria 45 (1997) 157-168.
%F A167237 Although A167237 is closely associated with the Wythoff array (A035513)
%F A167237 and Fibonacci numbers (A000045), it can be constructed independently.
%F A167237 First, construct the fractal sequence of the Wythoff array inductively
%F A167237 as described at A003603; then subtract 1 from all terms and delete
%F A167237 all 0s.
%e A167237 The first 7 rows in the construction of A003603 are
%e A167237 1
%e A167237 1
%e A167237 1 2
%e A167237 1 3 2
%e A167237 1 4 3 2 5
%e A167237 1 6 4 3 7 2 8 5
%e A167237 1 9 6 4 10 3 11 7 2 12 8 5 13
%e A167237 Subtracting 1 and deleting 0s leaves
%e A167237 1
%e A167237 2 1
%e A167237 3 2 1 4
%e A167237 5 4 2 6 1 7 4
%e A167237 8 5 3 9 2 10 6 1 11 7 4 12
%Y A167237 A003603, A019586, A035513.
%K A167237 nonn,new
%O A167237 1,2
%A A167237 Clark Kimberling (ck6(AT)evansville.edu), Oct 31 2009

%I A167224
%S A167224 7,23,11,2,109,89,61,191,167,47,307,199,19,503,487,463,431,223,151,71,
%T A167224 53,991,919,271,1327,1231,1187,547,431,307,1607,1559,1439,1367,1103,887,
%U A167224 503,359,47,2161,2053,1873,1621,1297,433,2719,2663,2383,1783,1223,1063
%N A167224 Table of primes of the form n^3 - k^2, 0<=k<=A077121(n).
%C A167224 Primes in A167222;
%C A167224 A161681 is the range of this table.
%H A167224 R. Zumkeller, <a href="b167224.txt">Table of n, a(n) for n = 1..10000</a>
%H A167224 R. Zumkeller, <a href="a161681.txt">Some Examples</a>
%e A167224 7;23,11,2;;109,89,61;191,167,47;307,199,19;503,487,... .
%K A167224 nonn,tabf,new
%O A167224 1,1
%A A167224 Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 31 2009

%I A167223
%S A167223 0,0,1,3,0,3,3,3,7,1,3,6,9,6,7,11,1,20,13,5,19,11,8,15,15,0,17,22,11,22,
%T A167223 16,7,39,28,8,29,1,12,31,22,16,46,33,13,32,30,13,58,43,0,47,22,28,49,39,
%U A167223 20,47,51,18,44,32,21,84,63,0,70,38,28,113,45,23,43,66,46,52,63,28,78
%N A167223 Number of primes of the form n^3 - k^2, 0<=k<=A077121(n).
%C A167223 Number of terms per row in the table of A167224;
%C A167223 a(n) <= A077121(n).
%H A167223 R. Zumkeller, <a href="b167223.txt">Table of n, a(n) for n = 0..500</a>
%e A167223 a(3) = #{27-4, 27-16, 27-25} = #{23, 11, 2} = 3;
%e A167223 a(4) = #{} = 0;
%e A167223 a(5) = #{125-16, 125-36, 125-64} = #{109, 89, 61} = 3.
%K A167223 nonn,new
%O A167223 0,4
%A A167223 Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 31 2009

%I A167222
%S A167222 0,1,0,8,7,4,27,26,23,18,11,2,64,63,60,55,48,39,28,15,0,125,124,121,116,
%T A167222 109,100,89,76,61,44,25,4,216,215,212,207,200,191,180,167,152,135,116,
%U A167222 95,72,47,20,343,342,339,334,327,318,307,294,279,262,243,222,199,174
%N A167222 Table T(n,k) = n^3 - k^2, 0 <= k <= A077121(n).
%C A167222 For primes see A167224.
%H A167222 R. Zumkeller, <a href="b167222.txt">Table of n, a(n) for n = 1..10000</a>
%e A167222 0;1,0;8,7,4;27,26,23,18,11,2;64,63,60,55,48,39, ... .
%K A167222 nonn,tabf,new
%O A167222 0,4
%A A167222 Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 31 2009

%I A156048
%S A156048 32377,10908137,34030327,4860035567,7656800897
%N A156048 Prime numbers n with property that (2^n+n^2) == 0 mod (n+2).
%K A156048 more,nonn,new
%O A156048 1,1
%A A156048 Zak Seidov (zakseidov(AT)yahoo.com), Oct 31 2009
%E A156048 a(5)=7656800897 from Zak Seidov (zakseidov(AT)yahoo.com), Oct 31 2009

%I A167234
%S A167234 1,2,3,4,3,6,4,5,5,6,3,7,5,8,8,9,3,10,4,7,8,6,3,13,7,7,5,11,3,11,4,9,7,
%T A167234 6,8,13,5,5,7,11,3,16,4,12,13,6,3,17,5,11,9,7,3,10,7,15,5,5,3,21,7,7,11,
%U A167234 11,7,14,4,7,7,16,3,13,5,10,13,7,8,14,4,17,7,6,3,23,9,8,5,13,3,19,8,12
%N A167234 Smallest number such that no two divisors of n are congruent modulo a(n).
%C A167234 What can we say about the asymptotic behavior of this sequence? Does it contain every integer > 2 infinitely often?
%C A167234 For n > 6, a(n) <= floor(n/2) + 1; but this seems to be a very crude estimate.
%o A167234 (PARI) alldiff(v)=v=vecsort(v);for(k=1,#v-1,if(v[k]==v[k+1],return(0)));1
%o A167234 a(n)=local(ds);ds=divisors(n);for(k=#ds,n,if(alldiff(vector(#ds,i,ds[i]%k)),return(k)))
%K A167234 nonn,new
%O A167234 1,2
%A A167234 Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Oct 31 2009

%I A167233
%S A167233 12345769,12346597,12354967,12356749,12356947,12357649,12359647,
%T A167233 12369547,12374569,12375469,12394567,12435679,12436597,12453769,
%U A167233 12453967,12457639,12457693,12459673,12463579,12463597,12469357
%N A167233 Prime anagrams of 12345769
%C A167233 There are exactly 4333 such primes from a(1..3)=12345769,12346597,12354967 to a(4331..4333)=97652413,97653421,97654321.
%t A167233 Select[FromDigits/@Permutations[{1,2,3,4,5,6,7,9}],PrimeQ]
%K A167233 base,fini,full,nonn,new
%O A167233 1,1
%A A167233 Zak Seidov (zakseidov(AT)yahoo.com), Oct 31 2009

%I A136096
%S A136096 3,1,11,2,13,1,0
%N A136096 Ratios of consecutive terms of A135060, or 0 if quotient is not an integer
%e A136096 a(8) = 1 because both A135060(7) and A135060(8) are 840
%Y A136096 Cf. A135060.
%K A136096 more,nonn,new
%O A136096 2,1
%A A136096 J. Lowell (jhbubby(AT)mindspring.com), May 10 2008
%E A136096 Changed definition. - J. Lowell (jhbubby(AT)mindspring.com), Oct 30 2009

%I A167072
%S A167072 12,6720,3110400,1423806720,651286330860,297900675072000,136260356109480876,
%T A167072 62325740425973498880,28507909150300692211200,13039570449847302883368000,
%U A167072 5964323676112090939594326348,2728092696767010687412666368000,1247834652562251646622689145644236
%N A167072 Number of spanning trees in G X P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {2, 5}, {3, 5}, {4, 5}}
%D A167072 F. Faase, On the number of specific spanning subgraphs of the graphs A X P_n, Ars Combin. 49 (1998), 129-154.
%H A167072 P. Raff, <a href="b167072.txt">Table of n, a(n) for n = 1..200</a>
%H A167072 F. Faase, <a href="http://www.iwriteiam.nl/Cpaper.zip">On the number of specific spanning subgraphs of the graphs G X P_n</a>, Preliminary version of paper that appeared in Ars Combin. 49 (1998), 129-154.
%H A167072 F. Faase, <a href="http://www.iwriteiam.nl/counting.html">Counting Hamilton cycles in product graphs</a>
%H A167072 F. Faase, <a href="http://www.iwriteiam.nl/Cresults.html">Results from the counting program</a>
%H A167072 F. Faase, <a href="http://home.wxs.nl/~faase009/counting.html">Counting Hamilton cycles in product graphs</a>
%H A167072 P. Raff, <a href="http://arxiv.org/abs/0809.2551">Spanning Trees in Grid Graphs</a>.
%H A167072 P. Raff, <a href="http://www.math.rutgers.edu/~praff/span/5/12-13-14-25-35-45/index.xml">Analysis of the Number of Spanning Trees of G x P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {2, 5}, {3, 5}, {4, 5}}.</a> Contains sequence, recurrence, generating function, and more.
%H A167072 P. Raff, <a href="http://www.myraff.com/projects/spanning-trees-in-grid-graphs">Analysis of the Number of Spanning Trees of Grid Graphs</a>.
%H A167072 <a href="Sindx_Tra.html#trees">Index entries for sequences related to trees</a>
%F A167072 a(n) = 525 a(n-1)
%F A167072 - 32415 a(n-2)
%F A167072 + 696920 a(n-3)
%F A167072 - 5936265 a(n-4)
%F A167072 + 19827675 a(n-5)
%F A167072 - 29313582 a(n-6)
%F A167072 + 19827675 a(n-7)
%F A167072 - 5936265 a(n-8)
%F A167072 + 696920 a(n-9)
%F A167072 - 32415 a(n-10)
%F A167072 + 525 a(n-11)
%F A167072 - a(n-12)
%F A167072 G.f.: -12x(x^10+35x^9-2385x^8+26040x^7-54030x^6+54030x^4-26040x^3+2385x^2-35x-1)/(x^12-525x^11+32415x^10-696920x^9+5936265x^8-19827675x^7+29313582x^6-19827675x^5+5936265x^4-696920x^3+32415x^2-525x+1)
%K A167072 nonn
%O A167072 1,1
%A A167072 Paul Raff (paul(AT)myraff.com)

%I A167071
%S A167071 4,1376,361860,92544256,23575404820,6002044445280,1527898117755412,388939442019315712,
%T A167071 99007542753465378420,25203122804459545322080,6415645979596681028789108,
%U A167071 1633151297922105531036929280,415731036835959295502046104100,105827485262836457484100780941664
%N A167071 Number of spanning trees in G X P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {2, 5}, {3, 5}}
%D A167071 F. Faase, On the number of specific spanning subgraphs of the graphs A X P_n, Ars Combin. 49 (1998), 129-154.
%H A167071 P. Raff, <a href="b167071.txt">Table of n, a(n) for n = 1..200</a>
%H A167071 P. Raff, <a href="http://arxiv.org/abs/0809.2551">Spanning Trees in Grid Graphs</a>.
%H A167071 P. Raff, <a href="http://www.math.rutgers.edu/~praff/span/5/12-13-14-25-35/index.xml">Analysis of the Number of Spanning Trees of G x P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {2, 5}, {3, 5}}.</a> Contains sequence, recurrence, generating function, and more.
%H A167071 P. Raff, <a href="http://www.myraff.com/projects/spanning-trees-in-grid-graphs">Analysis of the Number of Spanning Trees of Grid Graphs</a>.
%H A167071 F. Faase, <a href="http://www.iwriteiam.nl/Cpaper.zip">On the number of specific spanning subgraphs of the graphs G X P_n</a>, Preliminary version of paper that appeared in Ars Combin. 49 (1998), 129-154.
%H A167071 F. Faase, <a href="http://www.iwriteiam.nl/counting.html">Counting Hamilton cycles in product graphs</a>
%H A167071 F. Faase, <a href="http://www.iwriteiam.nl/Cresults.html">Results from the counting program</a>
%H A167071 <a href="Sindx_Tra.html#trees">Index entries for sequences related to trees</a>
%H A167071 F. Faase, <a href="http://home.wxs.nl/~faase009/counting.html">Counting Hamilton cycles in product graphs</a>
%F A167071 a(n) = 344 a(n-1)
%F A167071 - 25540 a(n-2)
%F A167071 + 745448 a(n-3)
%F A167071 - 10445708 a(n-4)
%F A167071 + 76194968 a(n-5)
%F A167071 - 303860988 a(n-6)
%F A167071 + 687124520 a(n-7)
%F A167071 - 899525622 a(n-8)
%F A167071 + 687124520 a(n-9)
%F A167071 - 303860988 a(n-10)
%F A167071 + 76194968 a(n-11)
%F A167071 - 10445708 a(n-12)
%F A167071 + 745448 a(n-13)
%F A167071 - 25540 a(n-14)
%F A167071 + 344 a(n-15)
%F A167071 - a(n-16)
%F A167071 G.f.: -4x(x^14-2331x^12+56416x^11-467115x^10+1546624x^9-1949983x^8+1949983x^6-1546624x^5+467115x^4-56416x^3+2331x^2-1)/(x^16-344x^15+25540x^14-745448x^13+10445708x^12-76194968x^11+303860988x^10-687124520x^9+899525622x^8-687124520x^7+303860988x^6-76194968x^5+10445708x^4-745448x^3+25540x^2-344x+1)
%K A167071 nonn
%O A167071 1,1
%A A167071 Paul Raff (paul(AT)myraff.com)

%I A167070
%S A167070 1,201,27872,3656793,474581525,61445719296,7951276371389,1028790034978377,
%T A167070 133107787044919648,17221739109190982025,2228177484370996025801,
%U A167070 288285215706960759705600,37298804748402271018820409,4825779209505263485071458889
%N A167070 Number of spanning trees in G X P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {2, 5}}
%D A167070 F. Faase, On the number of specific spanning subgraphs of the graphs A X P_n, Ars Combin. 49 (1998), 129-154.
%H A167070 P. Raff, <a href="b167070.txt">Table of n, a(n) for n = 1..200</a>
%H A167070 P. Raff, <a href="http://arxiv.org/abs/0809.2551">Spanning Trees in Grid Graphs</a>.
%H A167070 P. Raff, <a href="http://www.math.rutgers.edu/~praff/span/5/12-13-14-25/index.xml">Analysis of the Number of Spanning Trees of G x P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {2, 5}}.</a> Contains sequence, recurrence, generating function, and more.
%H A167070 P. Raff, <a href="http://www.myraff.com/projects/spanning-trees-in-grid-graphs">Analysis of the Number of Spanning Trees of Grid Graphs</a>.
%H A167070 F. Faase, <a href="http://www.iwriteiam.nl/Cpaper.zip">On the number of specific spanning subgraphs of the graphs G X P_n</a>, Preliminary version of paper that appeared in Ars Combin. 49 (1998), 129-154.
%H A167070 F. Faase, <a href="http://www.iwriteiam.nl/counting.html">Counting Hamilton cycles in product graphs</a>
%H A167070 F. Faase, <a href="http://www.iwriteiam.nl/Cresults.html">Results from the counting program</a>
%H A167070 <a href="Sindx_Tra.html#trees">Index entries for sequences related to trees</a>
%H A167070 F. Faase, <a href="http://home.wxs.nl/~faase009/counting.html">Counting Hamilton cycles in product graphs</a>
%F A167070 a(n) = 201 a(n-1)
%F A167070 - 11104 a(n-2)
%F A167070 + 259893 a(n-3)
%F A167070 - 3001225 a(n-4)
%F A167070 + 18824856 a(n-5)
%F A167070 - 67848270 a(n-6)
%F A167070 + 144802410 a(n-7)
%F A167070 - 186068896 a(n-8)
%F A167070 + 144802410 a(n-9)
%F A167070 - 67848270 a(n-10)
%F A167070 + 18824856 a(n-11)
%F A167070 - 3001225 a(n-12)
%F A167070 + 259893 a(n-13)
%F A167070 - 11104 a(n-14)
%F A167070 + 201 a(n-15)
%F A167070 - a(n-16)
%F A167070 G.f.: -x(x^14-1425x^12+26532x^11-180448x^10+545916x^9-661242x^8+661242x^6-545916x^5+180448x^4-26532x^3+1425x^2-1)/(x^16-201x^15+11104x^14-259893x^13+3001225x^12-18824856x^11+67848270x^10-144802410x^9+186068896x^8-144802410x^7+67848270x^6-18824856x^5+3001225x^4-259893x^3+11104x^2-201x+1)
%K A167070 nonn
%O A167070 1,2
%A A167070 Paul Raff (paul(AT)myraff.com)

%I A167069
%S A167069 3,1005,250848,60075885,14263332015,3379514561280,800337094071879,
%T A167069 189513130911442365,44873808170614072416,10625354802279238810125,
%U A167069 2515898969449422698378427,595720806457312484163072000,141056237447350542048435569739
%N A167069 Number of spanning trees in G X P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {2, 3}, {4, 5}}
%D A167069 F. Faase, On the number of specific spanning subgraphs of the graphs A X P_n, Ars Combin. 49 (1998), 129-154.
%H A167069 P. Raff, <a href="b167069.txt">Table of n, a(n) for n = 1..200</a>
%H A167069 P. Raff, <a href="http://arxiv.org/abs/0809.2551">Spanning Trees in Grid Graphs</a>.
%H A167069 P. Raff, <a href="http://www.math.rutgers.edu/~praff/span/5/12-13-14-23-45/index.xml">Analysis of the Number of Spanning Trees of G x P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {2, 3}, {4, 5}}.</a> Contains sequence, recurrence, generating function, and more.
%H A167069 P. Raff, <a href="http://www.myraff.com/projects/spanning-trees-in-grid-graphs">Analysis of the Number of Spanning Trees of Grid Graphs</a>.
%H A167069 F. Faase, <a href="http://www.iwriteiam.nl/Cpaper.zip">On the number of specific spanning subgraphs of the graphs G X P_n</a>, Preliminary version of paper that appeared in Ars Combin. 49 (1998), 129-154.
%H A167069 F. Faase, <a href="http://www.iwriteiam.nl/counting.html">Counting Hamilton cycles in product graphs</a>
%H A167069 F. Faase, <a href="http://www.iwriteiam.nl/Cresults.html">Results from the counting program</a>
%H A167069 <a href="Sindx_Tra.html#trees">Index entries for sequences related to trees</a>
%H A167069 F. Faase, <a href="http://home.wxs.nl/~faase009/counting.html">Counting Hamilton cycles in product graphs</a>
%F A167069 a(n) = 335 a(n-1)
%F A167069 - 26224 a(n-2)
%F A167069 + 744035 a(n-3)
%F A167069 - 10084457 a(n-4)
%F A167069 + 72968360 a(n-5)
%F A167069 - 295849710 a(n-6)
%F A167069 + 685799270 a(n-7)
%F A167069 - 909474816 a(n-8)
%F A167069 + 685799270 a(n-9)
%F A167069 - 295849710 a(n-10)
%F A167069 + 72968360 a(n-11)
%F A167069 - 10084457 a(n-12)
%F A167069 + 744035 a(n-13)
%F A167069 - 26224 a(n-14)
%F A167069 + 335 a(n-15)
%F A167069 - a(n-16)
%F A167069 G.f.: -3x(x^14-2385x^12+54940x^11-451104x^10+1542340x^9-2024890x^8+2024890x^6-1542340x^5+451104x^4-54940x^3+2385x^2-1)/(x^16-335x^15+26224x^14-744035x^13+10084457x^12-72968360x^11+295849710x^10-685799270x^9+909474816x^8-685799270x^7+295849710x^6-72968360x^5+10084457x^4-744035x^3+26224x^2-335x+1)
%K A167069 nonn
%O A167069 1,1
%A A167069 Paul Raff (paul(AT)myraff.com)

%I A167068
%S A167068 11,6061,2733511,1215842661,540144000000,239933520731861,106577890632874111,
%T A167068 47341582784338831461,21028987835540967334811,9341012640240002304000000,
%U A167068 4149249488236281570533713211,1843084039808720108847180812661,818692341198182161542031245824911
%N A167068 Number of spanning trees in G X P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 5}, {4, 5}}
%D A167068 F. Faase, On the number of specific spanning subgraphs of the graphs A X P_n, Ars Combin. 49 (1998), 129-154.
%H A167068 P. Raff, <a href="b167068.txt">Table of n, a(n) for n = 1..200</a>
%H A167068 P. Raff, <a href="http://arxiv.org/abs/0809.2551">Spanning Trees in Grid Graphs</a>.
%H A167068 P. Raff, <a href="http://www.math.rutgers.edu/~praff/span/5/12-13-14-23-25-45/index.xml">Analysis of the Number of Spanning Trees of G x P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 5}, {4, 5}}.</a> Contains sequence, recurrence, generating function, and more.
%H A167068 P. Raff, <a href="http://www.myraff.com/projects/spanning-trees-in-grid-graphs">Analysis of the Number of Spanning Trees of Grid Graphs</a>.
%H A167068 F. Faase, <a href="http://www.iwriteiam.nl/Cpaper.zip">On the number of specific spanning subgraphs of the graphs G X P_n</a>, Preliminary version of paper that appeared in Ars Combin. 49 (1998), 129-154.
%H A167068 F. Faase, <a href="http://www.iwriteiam.nl/counting.html">Counting Hamilton cycles in product graphs</a>
%H A167068 F. Faase, <a href="http://www.iwriteiam.nl/Cresults.html">Results from the counting program</a>
%H A167068 <a href="Sindx_Tra.html#trees">Index entries for sequences related to trees</a>
%H A167068 F. Faase, <a href="http://home.wxs.nl/~faase009/counting.html">Counting Hamilton cycles in product graphs</a>
%F A167068 a(n) = 551 a(n-1)
%F A167068 - 51500 a(n-2)
%F A167068 + 1873400 a(n-3)
%F A167068 - 31993500 a(n-4)
%F A167068 + 271314053 a(n-5)
%F A167068 - 1157139603 a(n-6)
%F A167068 + 2669595000 a(n-7)
%F A167068 - 3507446800 a(n-8)
%F A167068 + 2669595000 a(n-9)
%F A167068 - 1157139603 a(n-10)
%F A167068 + 271314053 a(n-11)
%F A167068 - 31993500 a(n-12)
%F A167068 + 1873400 a(n-13)
%F A167068 - 51500 a(n-14)
%F A167068 + 551 a(n-15)
%F A167068 - a(n-16)
%F A167068 G.f.: -11x(x^14-3600x^12+110200x^11-1112601x^10+3855898x^9-4841800x^8+4841800x^6-3855898x^5+1112601x^4-110200x^3+3600x^2-1)/(x^16-551x^15+51500x^14-1873400x^13+31993500x^12-271314053x^11+1157139603x^10-2669595000x^9+3507446800x^8-2669595000x^7+1157139603x^6-271314053x^5+31993500x^4-1873400x^3+51500x^2-551x+1)
%K A167068 nonn
%O A167068 1,1
%A A167068 Paul Raff (paul(AT)myraff.com)

%I A167067
%S A167067 3,969,232551,53799849,12372096000,2842087396401,652745210821239,149910861311886393,
%T A167067 34428589607251552779,7906872302105745408000,1815892322798648692785531,
%U A167067 417037814066206883492561817,95776899454583611992923575575,21996121549640772495096513751713
%N A167067 Number of spanning trees in G X P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 5}}
%D A167067 F. Faase, On the number of specific spanning subgraphs of the graphs A X P_n, Ars Combin. 49 (1998), 129-154.
%H A167067 P. Raff, <a href="b167067.txt">Table of n, a(n) for n = 1..200</a>
%H A167067 P. Raff, <a href="http://arxiv.org/abs/0809.2551">Spanning Trees in Grid Graphs</a>.
%H A167067 P. Raff, <a href="http://www.math.rutgers.edu/~praff/span/5/12-13-14-23-25/index.xml">Analysis of the Number of Spanning Trees of G x P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 5}}.</a> Contains sequence, recurrence, generating function, and more.
%H A167067 P. Raff, <a href="http://www.myraff.com/projects/spanning-trees-in-grid-graphs">Analysis of the Number of Spanning Trees of Grid Graphs</a>.
%H A167067 F. Faase, <a href="http://www.iwriteiam.nl/Cpaper.zip">On the number of specific spanning subgraphs of the graphs G X P_n</a>, Preliminary version of paper that appeared in Ars Combin. 49 (1998), 129-154.
%H A167067 F. Faase, <a href="http://www.iwriteiam.nl/counting.html">Counting Hamilton cycles in product graphs</a>
%H A167067 F. Faase, <a href="http://www.iwriteiam.nl/Cresults.html">Results from the counting program</a>
%H A167067 <a href="Sindx_Tra.html#trees">Index entries for sequences related to trees</a>
%H A167067 F. Faase, <a href="http://home.wxs.nl/~faase009/counting.html">Counting Hamilton cycles in product graphs</a>
%F A167067 a(n) = 323 a(n-1)
%F A167067 - 24404 a(n-2)
%F A167067 + 723520 a(n-3)
%F A167067 - 9950948 a(n-4)
%F A167067 + 71523505 a(n-5)
%F A167067 - 283937931 a(n-6)
%F A167067 + 637842312 a(n-7)
%F A167067 - 832457728 a(n-8)
%F A167067 + 637842312 a(n-9)
%F A167067 - 283937931 a(n-10)
%F A167067 + 71523505 a(n-11)
%F A167067 - 9950948 a(n-12)
%F A167067 + 723520 a(n-13)
%F A167067 - 24404 a(n-14)
%F A167067 + 323 a(n-15)
%F A167067 - a(n-16)
%F A167067 G.f.: -3x(x^14-2408x^12+54264x^11-439553x^10+1500658x^9-1911656x^8+1911656x^6-1500658x^5+439553x^4-54264x^3+2408x^2-1)/(x^16-323x^15+24404x^14-723520x^13+9950948x^12-71523505x^11+283937931x^10-637842312x^9+832457728x^8-637842312x^7+283937931x^6-71523505x^5+9950948x^4-723520x^3+24404x^2-323x+1)
%K A167067 nonn
%O A167067 1,1
%A A167067 Paul Raff (paul(AT)myraff.com)

%I A167066
%S A167066 24,20160,14515200,10373448960,7410329640120,5293465841664000,3781306797401609112,
%T A167066 2701118650243184317440,1929502759140378901785600,1378310758353447731649144000,
%U A167066 984575190426384431371033497336,703316214957312006365562863616000,502403171470887016026721609133115192
%N A167066 Number of spanning trees in G X P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 5}, {4, 5}}
%D A167066 F. Faase, On the number of specific spanning subgraphs of the graphs A X P_n, Ars Combin. 49 (1998), 129-154.
%H A167066 P. Raff, <a href="b167066.txt">Table of n, a(n) for n = 1..200</a>
%H A167066 P. Raff, <a href="http://arxiv.org/abs/0809.2551">Spanning Trees in Grid Graphs</a>.
%H A167066 P. Raff, <a href="http://www.math.rutgers.edu/~praff/span/5/12-13-14-23-24-35-45/index.xml">Analysis of the Number of Spanning Trees of G x P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 5}, {4, 5}}.</a> Contains sequence, recurrence, generating function, and more.
%H A167066 P. Raff, <a href="http://www.myraff.com/projects/spanning-trees-in-grid-graphs">Analysis of the Number of Spanning Trees of Grid Graphs</a>.
%H A167066 F. Faase, <a href="http://www.iwriteiam.nl/Cpaper.zip">On the number of specific spanning subgraphs of the graphs G X P_n</a>, Preliminary version of paper that appeared in Ars Combin. 49 (1998), 129-154.
%H A167066 F. Faase, <a href="http://www.iwriteiam.nl/counting.html">Counting Hamilton cycles in product graphs</a>
%H A167066 F. Faase, <a href="http://www.iwriteiam.nl/Cresults.html">Results from the counting program</a>
%H A167066 <a href="Sindx_Tra.html#trees">Index entries for sequences related to trees</a>
%H A167066 F. Faase, <a href="http://home.wxs.nl/~faase009/counting.html">Counting Hamilton cycles in product graphs</a>
%F A167066 a(n) = 840 a(n-1)
%F A167066 - 95522 a(n-2)
%F A167066 + 4231920 a(n-3)
%F A167066 - 87627601 a(n-4)
%F A167066 + 863951760 a(n-5)
%F A167066 - 3862082882 a(n-6)
%F A167066 + 9004563960 a(n-7)
%F A167066 - 11846119204 a(n-8)
%F A167066 + 9004563960 a(n-9)
%F A167066 - 3862082882 a(n-10)
%F A167066 + 863951760 a(n-11)
%F A167066 - 87627601 a(n-12)
%F A167066 + 4231920 a(n-13)
%F A167066 - 95522 a(n-14)
%F A167066 + 840 a(n-15)
%F A167066 - a(n-16)
%F A167066 G.f.: -24x(x^14-5278x^12+201600x^11-2458194x^10+8663760x^9-10786195x^8+10786195x^6-8663760x^5+2458194x^4-201600x^3+5278x^2-1)/(x^16-840x^15+95522x^14-4231920x^13+87627601x^12-863951760x^11+3862082882x^10-9004563960x^9+11846119204x^8-9004563960x^7+3862082882x^6-863951760x^5+87627601x^4-4231920x^3+95522x^2-840x+1)
%K A167066 nonn
%O A167066 1,1
%A A167066 Paul Raff (paul(AT)myraff.com)

%I A167065
%S A167065 8,4128,1688680,674251008,268240730440,106651712835360,42400091291143144,
%T A167065 16856142798678061056,6701134268084528945960,2664024512087857705508640,
%U A167065 1059078313836124682324459656,421034736344698799106102063360,167381624605785919658488535740200
%N A167065 Number of spanning trees in G X P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 5}}
%D A167065 F. Faase, On the number of specific spanning subgraphs of the graphs A X P_n, Ars Combin. 49 (1998), 129-154.
%H A167065 P. Raff, <a href="b167065.txt">Table of n, a(n) for n = 1..200</a>
%H A167065 P. Raff, <a href="http://arxiv.org/abs/0809.2551">Spanning Trees in Grid Graphs</a>.
%H A167065 P. Raff, <a href="http://www.math.rutgers.edu/~praff/span/5/12-13-14-23-24-35/index.xml">Analysis of the Number of Spanning Trees of G x P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 5}}.</a> Contains sequence, recurrence, generating function, and more.
%H A167065 P. Raff, <a href="http://www.myraff.com/projects/spanning-trees-in-grid-graphs">Analysis of the Number of Spanning Trees of Grid Graphs</a>.
%H A167065 F. Faase, <a href="http://www.iwriteiam.nl/Cpaper.zip">On the number of specific spanning subgraphs of the graphs G X P_n</a>, Preliminary version of paper that appeared in Ars Combin. 49 (1998), 129-154.
%H A167065 F. Faase, <a href="http://www.iwriteiam.nl/counting.html">Counting Hamilton cycles in product graphs</a>
%H A167065 F. Faase, <a href="http://www.iwriteiam.nl/Cresults.html">Results from the counting program</a>
%H A167065 <a href="Sindx_Tra.html#trees">Index entries for sequences related to trees</a>
%H A167065 F. Faase, <a href="http://home.wxs.nl/~faase009/counting.html">Counting Hamilton cycles in product graphs</a>
%F A167065 a(n) = 516 a(n-1)
%F A167065 - 51460 a(n-2)
%F A167065 + 1809612 a(n-3)
%F A167065 - 29405308 a(n-4)
%F A167065 + 244066452 a(n-5)
%F A167065 - 1071197628 a(n-6)
%F A167065 + 2573753820 a(n-7)
%F A167065 - 3447217942 a(n-8)
%F A167065 + 2573753820 a(n-9)
%F A167065 - 1071197628 a(n-10)
%F A167065 + 244066452 a(n-11)
%F A167065 - 29405308 a(n-12)
%F A167065 + 1809612 a(n-13)
%F A167065 - 51460 a(n-14)
%F A167065 + 516 a(n-15)
%F A167065 - a(n-16)
%F A167065 G.f.: -8x(x^14-3711x^12+105264x^11-1019095x^10+3723456x^9-4971063x^8+4971063x^6-3723456x^5+1019095x^4-105264x^3+3711x^2-1)/(x^16-516x^15+51460x^14-1809612x^13+29405308x^12-244066452x^11+1071197628x^10-2573753820x^9+3447217942x^8-2573753820x^7+1071197628x^6-244066452x^5+29405308x^4-1809612x^3+51460x^2-516x+1)
%K A167065 nonn
%O A167065 1,1
%A A167065 Paul Raff (paul(AT)myraff.com)

%I A167064
%S A167064 9,4725,1990656,822343725,338887026225,139607890329600,57510072475569441,
%T A167064 23690531503846057725,9758998421421748936704,4020088612537397612953125,
%U A167064 1656021591727120808594862489,682175884126257323680569753600,281013205982204002882115759532921
%N A167064 Number of spanning trees in G X P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {1, 5}, {2, 3}, {4, 5}}
%D A167064 F. Faase, On the number of specific spanning subgraphs of the graphs A X P_n, Ars Combin. 49 (1998), 129-154.
%H A167064 P. Raff, <a href="b167064.txt">Table of n, a(n) for n = 1..200</a>
%H A167064 P. Raff, <a href="http://arxiv.org/abs/0809.2551">Spanning Trees in Grid Graphs</a>.
%H A167064 P. Raff, <a href="http://www.math.rutgers.edu/~praff/span/5/12-13-14-15-23-45/index.xml">Analysis of the Number of Spanning Trees of G x P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {1, 5}, {2, 3}, {4, 5}}.</a> Contains sequence, recurrence, generating function, and more.
%H A167064 P. Raff, <a href="http://www.myraff.com/projects/spanning-trees-in-grid-graphs">Analysis of the Number of Spanning Trees of Grid Graphs</a>.
%H A167064 F. Faase, <a href="http://www.iwriteiam.nl/Cpaper.zip">On the number of specific spanning subgraphs of the graphs G X P_n</a>, Preliminary version of paper that appeared in Ars Combin. 49 (1998), 129-154.
%H A167064 F. Faase, <a href="http://www.iwriteiam.nl/counting.html">Counting Hamilton cycles in product graphs</a>
%H A167064 F. Faase, <a href="http://www.iwriteiam.nl/Cresults.html">Results from the counting program</a>
%H A167064 <a href="Sindx_Tra.html#trees">Index entries for sequences related to trees</a>
%H A167064 F. Faase, <a href="http://home.wxs.nl/~faase009/counting.html">Counting Hamilton cycles in product graphs</a>
%F A167064 a(n) = 504 a(n-1)
%F A167064 - 40152 a(n-2)
%F A167064 + 937188 a(n-3)
%F A167064 - 8104008 a(n-4)
%F A167064 + 27431208 a(n-5)
%F A167064 - 40609478 a(n-6)
%F A167064 + 27431208 a(n-7)
%F A167064 - 8104008 a(n-8)
%F A167064 + 937188 a(n-9)
%F A167064 - 40152 a(n-10)
%F A167064 + 504 a(n-11)
%F A167064 - a(n-12)
%F A167064 G.f.: -9x(x^10+21x^9-3264x^8+37401x^7-74299x^6+74299x^4-37401x^3+3264x^2-21x-1)/(x^12-504x^11+40152x^10-937188x^9+8104008x^8-27431208x^7+40609478x^6-27431208x^5+8104008x^4-937188x^3+40152x^2-504x+1)
%K A167064 nonn
%O A167064 1,1
%A A167064 Paul Raff (paul(AT)myraff.com)

%I A167063
%S A167063 21,16905,11515392,7766579625,5234202655605,3527304596766720,2377020102892371573,
%T A167063 1601852459790100499625,1079473906452564386072064,727447713589013080159967625,
%U A167063 490220442215546503112745464469,330355127203424593855513657344000,222623335689469074506271256084716693
%N A167063 Number of spanning trees in G X P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {1, 5}, {2, 3}, {2, 4}, {3, 5}}
%D A167063 F. Faase, On the number of specific spanning subgraphs of the graphs aX P_n, Ars Combin. 49 (1998), 129-154.
%H A167063 P. Raff, <a href="b167063.txt">Table of n, a(n) for n = 1..200</a>
%H A167063 F. Faase, <a href="http://www.iwriteiam.nl/Cpaper.zip">On the number of specific spanning subgraphs of the graphs G X P_n</a>, Preliminary version of paper that appeared in Ars Combin. 49 (1998), 129-154.
%H A167063 F. Faase, <a href="http://www.iwriteiam.nl/counting.html">Counting Hamilton cycles in product graphs</a>
%H A167063 F. Faase, <a href="http://www.iwriteiam.nl/Cresults.html">Results from the counting program</a>
%H A167063 F. Faase, <a href="http://home.wxs.nl/~faase009/counting.html">Counting Hamilton cycles in product graphs</a>
%H A167063 P. Raff, <a href="http://arxiv.org/abs/0809.2551">Spanning Trees in Grid Graphs</a>.
%H A167063 P. Raff, <a href="http://www.math.rutgers.edu/~praff/span/5/12-13-14-15-23-24-35/index.xml">Analysis of the Number of Spanning Trees of G x P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {1, 5}, {2, 3}, {2, 4}, {3, 5}}.</a> Contains sequence, recurrence, generating function, and more.
%H A167063 P. Raff, <a href="http://www.myraff.com/projects/spanning-trees-in-grid-graphs">Analysis of the Number of Spanning Trees of Grid Graphs</a>.
%H A167063 <a href="Sindx_Tra.html#trees">Index entries for sequences related to trees</a>
%F A167063 a(n) = 805 a(n-1)
%F A167063 - 94300 a(n-2)
%F A167063 + 4128845 a(n-3)
%F A167063 - 82955561 a(n-4)
%F A167063 + 801676960 a(n-5)
%F A167063 - 3659544950 a(n-6)
%F A167063 + 8726681390 a(n-7)
%F A167063 - 11584112776 a(n-8)
%F A167063 + 8726681390 a(n-9)
%F A167063 - 3659544950 a(n-10)
%F A167063 + 801676960 a(n-11)
%F A167063 - 82955561 a(n-12)
%F A167063 + 4128845 a(n-13)
%F A167063 - 94300 a(n-14)
%F A167063 + 805 a(n-15)
%F A167063 - a(n-16)
%F A167063 G.f.: -21x(x^14-5373x^12+196420x^11-2311184x^10+8452500x^9-10863790x^8+10863790x^6-8452500x^5+2311184x^4-196420x^3+5373x^2-1)/(x^16-805x^15+94300x^14-4128845x^13+82955561x^12-801676960x^11+3659544950x^10-8726681390x^9+11584112776x^8-8726681390x^7+3659544950x^6-801676960x^5+82955561x^4-4128845x^3+94300x^2-805x+1)
%K A167063 nonn,easy,mult
%O A167063 1,1
%A A167063 Paul Raff (paul(AT)myraff.com)

%I A167062
%S A167062 16,12096,7526400,4600399104,2805387952400,1710196656537600,1042505162050645904,
%T A167062 635487948490723808256,387378914569568374118400,236137288417488262321070400,
%U A167062 143943863916057463999036728976,87744870926093811441456945561600,53487256495669025156132129844140944
%N A167062 Number of spanning trees in G X P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {1, 5}, {2, 3}, {2, 4}, {3, 4}}
%D A167062 F. Faase, On the number of specific spanning subgraphs of the graphs aX P_n, Ars Combin. 49 (1998), 129-154.
%H A167062 P. Raff, <a href="b167062.txt">Table of n, a(n) for n = 1..200</a>
%H A167062 F. Faase, <a href="http://www.iwriteiam.nl/Cpaper.zip">On the number of specific spanning subgraphs of the graphs G X P_n</a>, Preliminary version of paper that appeared in Ars Combin. 49 (1998), 129-154.
%H A167062 F. Faase, <a href="http://www.iwriteiam.nl/counting.html">Counting Hamilton cycles in product graphs</a>
%H A167062 F. Faase, <a href="http://www.iwriteiam.nl/Cresults.html">Results from the counting program</a>
%H A167062 F. Faase, <a href="http://home.wxs.nl/~faase009/counting.html">Counting Hamilton cycles in product graphs</a>
%H A167062 P. Raff, <a href="http://arxiv.org/abs/0809.2551">Spanning Trees in Grid Graphs</a>.
%H A167062 P. Raff, <a href="http://www.math.rutgers.edu/~praff/span/5/12-13-14-15-23-24-34/index.xml">Analysis of the Number of Spanning Trees of G x P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {1, 5}, {2, 3}, {2, 4}, {3, 4}}.</a> Contains sequence, recurrence, generating function, and more.
%H A167062 <a href="Sindx_Tra.html#trees">Index entries for sequences related to trees</a>
%H A167062 P. Raff, <a href="http://www.myraff.com/projects/spanning-trees-in-grid-graphs">Analysis of the Number of Spanning Trees of Grid Graphs</a>.
%F A167062 a(n) = 735 a(n-1)
%F A167062 - 80115 a(n-2)
%F A167062 + 2269596 a(n-3)
%F A167062 - 23630145 a(n-4)
%F A167062 + 89290005 a(n-5)
%F A167062 - 139636406 a(n-6)
%F A167062 + 89290005 a(n-7)
%F A167062 - 23630145 a(n-8)
%F A167062 + 2269596 a(n-9)
%F A167062 - 80115 a(n-10)
%F A167062 + 735 a(n-11)
%F A167062 - a(n-12)
%F A167062 G.f.: -16x(x^10+21x^9-5145x^8+78288x^7-175246x^6+175246x^4-78288x^3+5145x^2-21x-1)/(x^12-735x^11+80115x^10-2269596x^9+23630145x^8-89290005x^7+139636406x^6-89290005x^5+23630145x^4-2269596x^3+80115x^2-735x+1)
%K A167062 nonn,easy,mult
%O A167062 1,1
%A A167062 Paul Raff (paul(AT)myraff.com)

%I A167061
%S A167061 40,47040,48384000,49461807360,50545351901000,51651393970176000,52781550346052950760,
%T A167061 53936428658183506928640,55116575633234676605184000,56322544581812152703647896000,
%U A167061 57554900528304912551898910864840,58814220831251084699615165546496000,60101095479875496770600392870888679560
%N A167061 Number of spanning trees in G X P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {1, 5}, {2, 3}, {2, 4}, {2, 5}, {3, 4}}
%D A167061 F. Faase, On the number of specific spanning subgraphs of the graphs A X P_n, Ars Combin. 49 (1998), 129-154.
%H A167061 P. Raff, <a href="b167061.txt">Table of n, a(n) for n = 1..200</a>
%H A167061 P. Raff, <a href="http://arxiv.org/abs/0809.2551">Spanning Trees in Grid Graphs</a>.
%H A167061 P. Raff, <a href="http://www.math.rutgers.edu/~praff/span/5/12-13-14-15-23-24-25-34/index.xml">Analysis of the Number of Spanning Trees of G x P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {1, 5}, {2, 3}, {2, 4}, {2, 5}, {3, 4}}.</a> Contains sequence, recurrence, generating function, and more.
%H A167061 P. Raff, <a href="http://www.myraff.com/projects/spanning-trees-in-grid-graphs">Analysis of the Number of Spanning Trees of Grid Graphs</a>.
%H A167061 F. Faase, <a href="http://www.iwriteiam.nl/Cpaper.zip">On the number of specific spanning subgraphs of the graphs G X P_n</a>, Preliminary version of paper that appeared in Ars Combin. 49 (1998), 129-154.
%H A167061 F. Faase, <a href="http://www.iwriteiam.nl/counting.html">Counting Hamilton cycles in product graphs</a>
%H A167061 F. Faase, <a href="http://www.iwriteiam.nl/Cresults.html">Results from the counting program</a>
%H A167061 <a href="Sindx_Tra.html#trees">Index entries for sequences related to trees</a>
%H A167061 F. Faase, <a href="http://home.wxs.nl/~faase009/counting.html">Counting Hamilton cycles in product graphs</a>
%F A167061 a(n) = 1152 a(n-1)
%F A167061 - 138048 a(n-2)
%F A167061 + 5263416 a(n-3)
%F A167061 - 72792384 a(n-4)
%F A167061 + 279916416 a(n-5)
%F A167061 - 429599666 a(n-6)
%F A167061 + 279916416 a(n-7)
%F A167061 - 72792384 a(n-8)
%F A167061 + 5263416 a(n-9)
%F A167061 - 138048 a(n-10)
%F A167061 + 1152 a(n-11)
%F A167061 - a(n-12)
%F A167061 G.f.: -40x(x^10+24x^9-7104x^8+167016x^7-378475x^6+378475x^4-167016x^3+7104x^2-24x-1)/(x^12-1152x^11+138048x^10-5263416x^9+72792384x^8-279916416x^7+429599666x^6-279916416x^5+72792384x^4-5263416x^3+138048x^2-1152x+1)
%K A167061 nonn
%O A167061 1,1
%A A167061 Paul Raff (paul(AT)myraff.com)

%I A167060
%S A167060 20,15680,10368000,6788875520,4442379540500,2906788405248000,1901996646002328980,
%T A167060 1244531724569497441280,814333290473214499968000,532841946954369840453512000,
%U A167060 348653977101113682528774921620,228134433564164121977905348608000,149274992387437573877742622270584980
%N A167060 Number of spanning trees in G X P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {1, 5}, {2, 3}, {2, 4}, {2, 5}}
%D A167060 F. Faase, On the number of specific spanning subgraphs of the graphs A X P_n, Ars Combin. 49 (1998), 129-154.
%H A167060 P. Raff, <a href="b167060.txt">Table of n, a(n) for n = 1..200</a>
%H A167060 P. Raff, <a href="http://arxiv.org/abs/0809.2551">Spanning Trees in Grid Graphs</a>.
%H A167060 P. Raff, <a href="http://www.math.rutgers.edu/~praff/span/5/12-13-14-15-23-24-25/index.xml">Analysis of the Number of Spanning Trees of G x P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {1, 5}, {2, 3}, {2, 4}, {2, 5}}.</a> Contains sequence, recurrence, generating function, and more.
%H A167060 P. Raff, <a href="http://www.myraff.com/projects/spanning-trees-in-grid-graphs">Analysis of the Number of Spanning Trees of Grid Graphs</a>.
%H A167060 F. Faase, <a href="http://www.iwriteiam.nl/Cpaper.zip">On the number of specific spanning subgraphs of the graphs G X P_n</a>, Preliminary version of paper that appeared in Ars Combin. 49 (1998), 129-154.
%H A167060 F. Faase, <a href="http://www.iwriteiam.nl/counting.html">Counting Hamilton cycles in product graphs</a>
%H A167060 F. Faase, <a href="http://www.iwriteiam.nl/Cresults.html">Results from the counting program</a>
%H A167060 <a href="Sindx_Tra.html#trees">Index entries for sequences related to trees</a>
%H A167060 F. Faase, <a href="http://home.wxs.nl/~faase009/counting.html">Counting Hamilton cycles in product graphs</a>
%F A167060 a(n) = 720 a(n-1)
%F A167060 - 43920 a(n-2)
%F A167060 + 624783 a(n-3)
%F A167060 - 2247840 a(n-4)
%F A167060 + 2247840 a(n-5)
%F A167060 - 624783 a(n-6)
%F A167060 + 43920 a(n-7)
%F A167060 - 720 a(n-8)
%F A167060 + a(n-9)
%F A167060 G.f.: -20x(x^7+64x^6-2160x^5+4273x^4+4273x^3-2160x^2+64x+1)/(x^9-720x^8+43920x^7-624783x^6+2247840x^5-2247840x^4+624783x^3-43920x^2+720x-1)
%K A167060 nonn
%O A167060 1,1
%A A167060 Paul Raff (paul(AT)myraff.com)

%I A167059
%S A167059 8,4032,1612800,631427328,246562692200,96244833484800,37566939748080392,
%T A167059 14663279200231130112,5723424260979717196800,2233987356983360324068800,
%U A167059 871977888467614764819315368,340353508793721676084268236800,132847991246505889127220947758952
%N A167059 Number of spanning trees in G X P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {1, 5}, {2, 3}, {2, 4}}
%D A167059 F. Faase, On the number of specific spanning subgraphs of the graphs A X P_n, Ars Combin. 49 (1998), 129-154.
%H A167059 P. Raff, <a href="b167059.txt">Table of n, a(n) for n = 1..200</a>
%H A167059 P. Raff, <a href="http://arxiv.org/abs/0809.2551">Spanning Trees in Grid Graphs</a>.
%H A167059 P. Raff, <a href="http://www.math.rutgers.edu/~praff/span/5/12-13-14-15-23-24/index.xml">Analysis of the Number of Spanning Trees of G x P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {1, 5}, {2, 3}, {2, 4}}.</a> Contains sequence, recurrence, generating function, and more.
%H A167059 P. Raff, <a href="http://www.myraff.com/projects/spanning-trees-in-grid-graphs">Analysis of the Number of Spanning Trees of Grid Graphs</a>.
%H A167059 F. Faase, <a href="http://www.iwriteiam.nl/Cpaper.zip">On the number of specific spanning subgraphs of the graphs G X P_n</a>, Preliminary version of paper that appeared in Ars Combin. 49 (1998), 129-154.
%H A167059 F. Faase, <a href="http://www.iwriteiam.nl/counting.html">Counting Hamilton cycles in product graphs</a>
%H A167059 F. Faase, <a href="http://www.iwriteiam.nl/Cresults.html">Results from the counting program</a>
%H A167059 <a href="Sindx_Tra.html#trees">Index entries for sequences related to trees</a>
%H A167059 F. Faase, <a href="http://home.wxs.nl/~faase009/counting.html">Counting Hamilton cycles in product graphs</a>
%F A167059 a(n) = 504 a(n-1)
%F A167059 - 48706 a(n-2)
%F A167059 + 1765008 a(n-3)
%F A167059 - 29021617 a(n-4)
%F A167059 + 239655024 a(n-5)
%F A167059 - 1039298722 a(n-6)
%F A167059 + 2447629128 a(n-7)
%F A167059 - 3242171236 a(n-8)
%F A167059 + 2447629128 a(n-9)
%F A167059 - 1039298722 a(n-10)
%F A167059 + 239655024 a(n-11)
%F A167059 - 29021617 a(n-12)
%F A167059 + 1765008 a(n-13)
%F A167059 - 48706 a(n-14)
%F A167059 + 504 a(n-15)
%F A167059 - a(n-16)
%F A167059 G.f.: -8x(x^14-3710x^12+104832x^11-997954x^10+3633840x^9-4759203x^8+4759203x^6-3633840x^5+997954x^4-104832x^3+3710x^2-1)/(x^16-504x^15+48706x^14-1765008x^13+29021617x^12-239655024x^11+1039298722x^10-2447629128x^9+3242171236x^8-2447629128x^7+1039298722x^6-239655024x^5+29021617x^4-1765008x^3+48706x^2-504x+1)
%K A167059 nonn
%O A167059 1,1
%A A167059 Paul Raff (paul(AT)myraff.com)

%I A167058
%S A167058 3,945,221184,50055705,11275732875,2538325278720,571357349020731,
%T A167058 128606300878893705,28947814696524275712,6515821689652895090625,
%U A167058 1466636804229895456081107,330123137841949620861665280,74306935243221668928140352051
%N A167058 Number of spanning trees in (S_5 + e) X P_n.
%D A167058 F. Faase, On the number of specific spanning subgraphs of the graphs A X P_n, Ars Combin. 49 (1998), 129-154.
%H A167058 P. Raff, <a href="b167058.txt">Table of n, a(n) for n = 1..200</a>
%H A167058 F. Faase, <a href="http://www.iwriteiam.nl/Cpaper.zip">On the number of specific spanning subgraphs of the graphs G X P_n</a>, Preliminary version of paper that appeared in Ars Combin. 49 (1998), 129-154.
%H A167058 F. Faase, <a href="http://www.iwriteiam.nl/counting.html">Counting Hamilton cycles in product graphs</a>
%H A167058 F. Faase, <a href="http://www.iwriteiam.nl/Cresults.html">Results from the counting program</a>
%H A167058 F. Faase, <a href="http://home.wxs.nl/~faase009/counting.html">Counting Hamilton cycles in product graphs</a>
%H A167058 P. Raff, <a href="http://arxiv.org/abs/0809.2551">Spanning Trees in Grid Graphs</a>.
%H A167058 P. Raff, <a href="http://www.math.rutgers.edu/~praff/span/5/12-13-14-15-23/index.xml">Analysis of the Number of Spanning Trees of (S_5 + e) x P_n</a>. Contains sequence, recurrence, generating function, and more.
%H A167058 P. Raff, <a href="http://www.myraff.com/projects/spanning-trees-in-grid-graphs">Analysis of the Number of Spanning Trees of Grid Graphs</a>.
%H A167058 <a href="Sindx_Tra.html#trees">Index entries for sequences related to trees</a>
%F A167058 a(n) = 270 a(n-1)
%F A167058 - 10529 a(n-2)
%F A167058 + 95310 a(n-3)
%F A167058 - 177156 a(n-4)
%F A167058 + 95310 a(n-5)
%F A167058 - 10529 a(n-6)
%F A167058 + 270 a(n-7)
%F A167058 - a(n-8)
%F A167058 G.f.: -3x(x^6+45x^5-793x^4+793x^2-45x-1)/(x^8-270x^7+10529x^6-95310x^5+177156x^4-95310x^3+10529x^2-270x+1)
%K A167058 nonn
%O A167058 1,1
%A A167058 Paul Raff (paul(AT)myraff.com)

%I A167232
%S A167232 1,1,2,2,3,3,4,4,5,4,4,5
%V A167232 1,-1,2,-2,3,-3,4,-4,5,4,4,5
%N A167232 a(n) is the number obtained by writing out numbers from 1 to n and placing an alternate + and - minus sign between successive digits and evaluating the expression written.
%H A167232 Sphere Online Judge, <a href="http://www.spoj.pl/problems/KPSUM/">Problem 1433: The Sum</a> [Link edited by njas, Nov 02 2009]
%K A167232 sign,new,base
%O A167232 1,3
%A A167232 Dhruv (dhruvbird(AT)gmail.com), Oct 31 2009

%I A167231
%S A167231 123,2345,3456,4567,5678,6789,7890,8901,9012,10123,11234,12345,13456,
%T A167231 14567,15678,16789,17890,18901,19012,20123,21234,22345,23456
%N A167231 Append three digits, each increasing by one modulo 10 from the last digit the of the positive integers. 0 -> 123, 1 -> 1234 2 -> 2345, ... , 9 -> 9012, 10 ->10123, etc.
%K A167231 easy,nonn,new
%O A167231 0,1
%A A167231 Felix Tubiana (fat2(AT)columbia.edu), Oct 30 2009

%I A167230
%S A167230 1,1,1,1,0,1,2,1,1,1,1,0,0,0,1,2,1,0,0,1,1,2,0,1,0,1,0,1,5,2,2,1,2,1,1,
%T A167230 1,1,0,0,0,0,0,0,0,1,2,1,0,0,0,0,0,0,1,1,2,0,1,0,0,0,0,0,1,0,1,5,2,2,1,
%U A167230 0,0,0,0,2,1,1,1,2,0,0,0,1,0,0,0,1,0,0,0,1,5,2,0,0,2,1,0,0,2,1,0,0,1,1
%N A167230 The matrix exponential of Sierpinski's triangle (A047999) scaled by exp(-1).
%C A167230 Conjecture: All the non-zero entries in this triangle are Bell numbers (A000110).
%e A167230 Triangle begins:
%e A167230 1
%e A167230 1 1
%e A167230 1 0 1
%e A167230 2 1 1 1
%e A167230 1 0 0 0 1
%e A167230 2 1 0 0 1 1
%e A167230 2 0 1 0 1 0 1
%e A167230 5 2 2 1 2 1 1 1
%e A167230 1 0 0 0 0 0 0 0 1
%e A167230 2 1 0 0 0 0 0 0 1 1
%e A167230 2 0 1 0 0 0 0 0 1 0 1
%e A167230 5 2 2 1 0 0 0 0 2 1 1 1
%e A167230 2 0 0 0 1 0 0 0 1 0 0 0 1
%e A167230 5 2 0 0 2 1 0 0 2 1 0 0 1 1
%o A167230 (PARI) matexp(M) = sum(k=0,99,1./k!*M^k); matexps(M) = matexp(M)/exp(1);
%o A167230 matexpsb(M) = bestappr(matexps(M),9999);
%o A167230 P = matpascal(13); S = matrix(14,14, n,k, P[n,k]%p);
%o A167230 SS = matexpsb(S);
%o A167230 for(n=1,14,for(k=1,n,print1(SS[n,k]," "));print(""))
%Y A167230 A047999, A000110
%K A167230 easy,nonn,tabl,new
%O A167230 0,7
%A A167230 Gerald McGarvey (gerald.mcgarvey(AT)comcast.net), Oct 30 2009

%I A167229
%S A167229 0,0,1,1,2,4,6,8,15,16,24,33,40,48,69,73,92,114,130,148,191,198,234,276,
%T A167229 304,332,407,421,476,550,584,631,748,760,857,956,1002,1070,1239
%N A167229 Number of 4-self-hedrites with n vertices.
%C A167229 From Table 2, p.11, of Sikiric. Number of 2-self-hedrites with 4 <= n <= 40 and and 2 <= i <= 4. An i-hedrite is a 4-regular plane graph with faces of size 2, 3 and 4. We do a short survey of their known properties and explain some new algorithms that allow their efficient enumeration. Using this we give the symmetry groups of all i-hedrites and the minimal representative for each. We also review the link of 4-hedrites with knot theory and the classification of 4-hedrites with simple central circuits. An i-self-hedrite is a self-dual plane graph with faces and vertices of size/degree 2, 3 and 4. We give a new efficient algorithm for enumerating them based on i-hedrites. We give a classification of their possible symmetry groups and a classification of 4-self-hedrites of symmetry T, Td in terms of the Goldberg-Coxeter construction. Then we give a method for enumerating 4-self-hedrites with simple zigzags.
%H A167229 Mathieu Dutour Sikiric, Michel Deza, <a href="http://arxiv.org/abs/0910.5323">4-regular and self-dual analogs of fullerenes</a>, Oct 28, 2009.
%Y A167229 Cf. A167156-A167160, A167227, A167228.
%K A167229 nonn,new
%O A167229 2,5
%A A167229 Jonathan Vos Post (jvospost3(AT)gmail.com), Oct 30 2009

%I A167228
%S A167228 0,1,1,4,6,7,11,16,16,26,29,30,42,47,48,64,72,70,89,104,90,119,131,124,
%T A167228 162,170,158,190,210,202,239,256,232,290,308,286,342,359,332
%N A167228 Number of 3-self-hedrites with n vertices.
%C A167228 From Table 2, p.11, of Sikiric. Number of 2-self-hedrites with 4 <= n <= 40 and and 2 <= i <= 4. An i-hedrite is a 4-regular plane graph with faces of size 2, 3 and 4. We do a short survey of their known properties and explain some new algorithms that allow their efficient enumeration. Using this we give the symmetry groups of all i-hedrites and the minimal representative for each. We also review the link of 4-hedrites with knot theory and the classification of 4-hedrites with simple central circuits. An i-self-hedrite is a self-dual plane graph with faces and vertices of size/degree 2, 3 and 4. We give a new efficient algorithm for enumerating them based on i-hedrites. We give a classification of their possible symmetry groups and a classification of 4-self-hedrites of symmetry T, Td in terms of the Goldberg-Coxeter construction. Then we give a method for enumerating 4-self-hedrites with simple zigzags.
%H A167228 Mathieu Dutour Sikiric, Michel Deza, <a href="http://arxiv.org/abs/0910.5323">4-regular and self-dual analogs of fullerenes</a>, Oct 28, 2009.
%Y A167228 Cf. A167156-A167160, A167227, A167229.
%K A167228 nonn,new
%O A167228 2,4
%A A167228 Jonathan Vos Post (jvospost3(AT)gmail.com), Oct 30 2009

%I A167227
%S A167227 1,1,2,2,3,3,3,3,5,4,4,6,5,5,8,5,6,8,6,8,10,7,7,10,10,8,12,10,9,14,9,9,
%T A167227 14,10,14,16,11,11,16
%N A167227 Number of 2-self-hedrites with n vertices.
%C A167227 From Table 2, p.11, of Sikiric. Number of 2-self-hedrites with 4 <= n <= 40 and and 2 <= i <= 4. An i-hedrite is a 4-regular plane graph with faces of size 2, 3 and 4. We do a short survey of their known properties and explain some new algorithms that allow their efficient enumeration. Using this we give the symmetry groups of all i-hedrites and the minimal representative for each. We also review the link of 4-hedrites with knot theory and the classification of 4-hedrites with simple central circuits. An i-self-hedrite is a self-dual plane graph with faces and vertices of size/degree 2, 3 and 4. We give a new efficient algorithm for enumerating them based on i-hedrites. We give a classification of their possible symmetry groups and a classification of 4-self-hedrites of symmetry T, Td in terms of the Goldberg-Coxeter construction. Then we give a method for enumerating 4-self-hedrites with simple zigzags.
%H A167227 Mathieu Dutour Sikiric, Michel Deza, <a href="http://arxiv.org/abs/0910.5323">4-regular and self-dual analogs of fullerenes</a>, Oct 28, 2009.
%Y A167227 Cf. A167156-A167160, A167228, A167229.
%K A167227 nonn,new
%O A167227 2,3
%A A167227 Jonathan Vos Post (jvospost3(AT)gmail.com), Oct 30 2009

%I A156038
%S A156038 1,32377,484177,3094247,10908137,15612137,16750127,17363927,24827519,
%T A156038 34030327,184923407,219087767,240654017,430450337,814220815,989880257,
%U A156038 1040713247,1257956527,1839451007
%N A156038 Odd numbers n with property that (2^n+n^2) == 0 mod (n+2).
%C A156038 Odd terms in A114977.
%Y A156038 Cf. A114977.
%K A156038 nonn,new
%O A156038 1,2
%A A156038 Zak Seidov (zakseidov(AT)yahoo.com), Oct 30 2009

%I A167140
%S A167140 1,4,24,416,34400,13561728,22961051392,160934805885952,
%T A167140 4612329945733989888,537318814887463743641600,
%U A167140 253532269357851227988228362240,483356648964255814869226601582346240
%N A167140 Self-convolution of A155200.
%F A167140 G.f.: A(x) = exp( Sum_{n>=1} 2^(n^2+1)*x^n/n ).
%F A167140 a(n) = (1/n)*Sum_{k=1..n} 2^(k^2+1)*a(n-k), a(0) = 1.
%e A167140 G.f.: A(x) = 1 + 4*x + 24*x^2 + 416*x^3 + 34400*x^4 + 13561728*x^5 +...
%e A167140 A(x)^(1/2) = 1 + 2*x + 10*x^2 + 188*x^3 + 16774*x^4 + 6745436*x^5 +...
%e A167140 log(A(x)) = 2^2*x + 2^5*x^2/2 + 2^10*x^3/3 + 2^17*x^4/4 + 2^26*x^5/5 +...
%o A167140 (PARI) {a(n)=polcoeff(exp( 2*sum(k=1, n, 2^(k^2)*x^k/k)+x*O(x^n)), n)}
%o A167140 (PARI) {a(n)=if(n==0, 1, (1/n)*sum(k=1, n, 2^(k^2+1)*a(n-k)))}
%Y A167140 Cf. A155200.
%K A167140 nonn,new
%O A167140 0,2
%A A167140 Paul D. Hanna (pauldhanna(AT)juno.com), Oct 30 2009

%I A165701
%S A165701 2,4,5,6,10,53,76,82,88,242,247,473,586,966,1015,1297,1825,2413,2599,
%T A165701 2833,5850,5965,6052
%N A165701 Numbers n such that 5^n-6 is prime.
%C A165701 Numbers corresponding to the a(n) for n>11 are probable prime.
%C A165701 There is no further term up to 8888.
%C A165701 If Q is a 4-perfect number and gcd(Q, 5*(5^a(n)-6))=1 then m=5^(a(n)-1)
%C A165701 (5^a(n)-6)*Q is a solution of the equation Iƒ(x)=5(x+Q)(see comment lines
%C A165701 of the sequence A058959). 142990848 is the smallest 4-perfect number m
%C A165701 such that 5 doesn't divide m.
%t A165701 Do[If[PrimeQ[5^n-6],Print[n]],{n,8888}]
%Y A165701 Cf. A007691, A054030, A058959.
%K A165701 more,nonn,new
%O A165701 1,1
%A A165701 M. F. Hasler and F. Firoozbakht (mymontain(AT)yahoo.com), Oct 30 2009

%I A167221
%S A167221 3,5,3,10,21,9,17,44,34,91,7
%N A167221 Numbers B such that (p_m ^ a_m)*(p_m-1 ^ a_m-1)*...*(3^a_1)*(2^a_0) = (B^m)*a_m + (B^m-1)*a_m-1 +...+ (B^1)*a_1 + (B^0)*a_0 where n =(p_m ^ a_m)*(p_m-1 ^ a_m-1)*...*(3^a_1)*(2^a_0) ; a_m >= 1 ; a_(i<m) >=0 ; p_0,p_1,..., p_m are prime numbers ; a_0, a_1, ..., a_m , B are integers . For B = (2^r)*3 - r we have n = (2^r)*3 .
%C A167221 B is the base in which we can express n like a sum{i=0 to m : B^i * a_i}. There is an isomorphism between (Z[B],+) and the positive rationals as the polynomials with integer coefficients considered as a group under addition are isomorphic to the positive rationals considered as a group under multiplication.
%e A167221 Ex_1 : n = 21 = 2^0 * 3^1 * 5^0 * 7^1 ; n = B^0 * 0 + B^1 * 1 + B^2 * 0 + B^3 * 1 ; so we have to solve the equation 21 = B + B^3 for an integer B. No such B does exist. Ex_2: n = 10 = 2^1 * 3^0 * 5^1 ; n = B^0 * 1 + B^1 * 0 + B^2 * 1 ; so we have to solve the equation 10 = 1 + B^2 for an integer B. B = +-3 . Ex_3: n = 12 = 2^2 * 3^1 ; n = B^0 * 2 + B^1 * 1 ; so we have to solve the equation 12 = 2 + B for an integer B. B = 10. Are there any other numbers besides n=12 in base 10 ?
%Y A167221 Cf. A054841, A054842
%K A167221 easy,nonn,new
%O A167221 1,1
%A A167221 Ctibor O. Zizka (c.zizka(AT)email.cz), Oct 30 2009

%I A167220
%S A167220 0,3,15,630,1830,2346,4371,5253,5460,19110,98346,478731,519690,1216020,
%T A167220 10669890,266539416,311737965,377836305,4375193196,5476282185
%N A167220 Triangular numbers that remain triangular numbers when their reverse is added.
%F A167220 {A000217(i) : A000217(i)+A004158(i) in A000217} [R. J. Mathar, Oct 31 2009].
%e A167220 2346 is a triangular number and 2346 + 6432 = 8778 is also a triangular number.
%p A167220 read("transforms"): A000217 := proc(n) n*(n+1)/2 ; end proc:
%p A167220 isA000217 := proc(n) issqr( 1+8*n) ; end proc:
%p A167220 isA167220 := proc(n) R := digrev(n) ; return isA000217(n) and isA000217(n+R) ; end:
%p A167220 for n from 0 to 30000 do T := A000217(n) ; if isA167220(T) then printf("%d,",T) ; end if; od: # R. J. Mathar, Oct 31 2009
%K A167220 base,nonn,new
%O A167220 1,2
%A A167220 Claudio L Meller (claudiomeller(AT)gmail.com), Oct 30 2009
%E A167220 5 more terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 31 2009

%I A167219
%S A167219 3,6,10,12,24,27,36,48,71,96,100
%N A167219 Numbers n such that (p_m ^ a_m)*(p_m-1 ^ a_m-1)*...*(3^a_1)*(2^a_0) = (B^m)*a_m + (B^m-1)*a_m-1 +...+ (B^1)*a_1 + (B^0)*a_0 where n =(p_m ^ a_m)*(p_m-1 ^ a_m-1)*...*(3^a_1)*(2^a_0) ; a_m >= 1 ; a_(i<m) >=0 ; p_0,p_1,..., p_m are prime numbers ; a_0, a_1, ..., a_m , B are integers . For n = (2^r)*3 we have B = (2^r)*3 - r.
%C A167219 B is the base in which we can express n like a sum{i=0 to m : B^i * a_i}. There is an isomorphism between (Z[B],+) and the positive rationals as the polynomials with integer coefficients considered as a group under addition are isomorphic to the positive rationals considered as a group under multiplication.
%e A167219 Ex_1 : n = 21 = 2^0 * 3^1 * 5^0 * 7^1 ; n = B^0 * 0 + B^1 * 1 + B^2 * 0 + B^3 * 1 ; so we have to solve the equation 21 = B + B^3 for an integer B. No such B does exist. Ex_2: n = 10 = 2^1 * 3^0 * 5^1 ; n = B^0 * 1 + B^1 * 0 + B^2 * 1 ; so we have to solve the equation 10 = 1 + B^2 for an integer B. B = +-3 . Ex_3: n = 12 = 2^2 * 3^1 ; n = B^0 * 2 + B^1 * 1 ; so we have to solve the equation 12 = 2 + B for an integer B. B = 10. Are there any other numbers besides n=12 in base 10 ?
%Y A167219 Cf. A054841, A054842
%K A167219 easy,nonn,new
%O A167219 1,1
%A A167219 Ctibor O. Zizka (c.zizka(AT)email.cz), Oct 30 2009

%I A167218
%S A167218 2,5,71,73,101,109,263,269,523,541,587,1061,1063,2089,2251,2273,2297,
%T A167218 2843,2861,5441,5477,5483,6203,6221,7129,7507,7937,10009,10163,10169,
%U A167218 10487,10691,20201,20693,22391,22769,24023,24877,26141,26171,26723
%N A167218 Primes such their reversal - 1 is a square
%C A167218 71 is prime and 17-1 = 16 = 4^2
%K A167218 base,nonn,new
%O A167218 1,1
%A A167218 Claudio L Meller (claudiomeller(AT)gmail.com), Oct 30 2009

%I A167217
%S A167217 3,53,827,3671,5507,8423,8693,30293,42083,42281,42299,53639,57203,59921,
%T A167217 80819
%N A167217 Primes such their reversal + 1 is a square
%C A167217 53 is prime and 35+1 = 36 = 6^2
%K A167217 base,nonn,new
%O A167217 1,1
%A A167217 Claudio L Meller (claudiomeller(AT)gmail.com), Oct 30 2009

%I A167216
%S A167216 3,23,41,47,83,89,233,251,257,281,401,461,491,809,821,827,839,857,863,
%T A167216 887,2003,2069,2081,2099,2153,2213,2237,2267,2333,2351,2381,2393,2399,
%U A167216 2477,2591,2633,2657,2711,2741,2753,2789,2819,2879,2909,2939,2957,2963
%N A167216 Primes such their reversal - 1 is also prime
%C A167216 23 is prime and 32-1= 31 is prime
%K A167216 base,nonn,new
%O A167216 1,1
%A A167216 Claudio L Meller (claudiomeller(AT)gmail.com), Oct 30 2009

%I A167215
%S A167215 2,61,211,271,277,283,601,613,631,643,661,691,829,853,883,2011,2017,
%T A167215 2029,2083,2089,2143,2161,2203,2221,2239,2251,2269,2281,2287,2293,2341,
%U A167215 2347,2371,2383,2389,2467,2551,2683,2719,2731,2749,2767,2791,2803,2851
%N A167215 Primes such that their reversal + 1 is also prime
%C A167215 61 is prime and 16+1= 17 is also a prime
%K A167215 base,nonn,new
%O A167215 1,1
%A A167215 Claudio L Meller (claudiomeller(AT)gmail.com), Oct 30 2009

%I A167214
%S A167214 2,10,30,68,140,246,406,616,900,1290,1760,2364,3094,3934,4920,6096,7480,
%T A167214 9018,10792,12780,14952,17402,20102,23112,26500,30186,34128,38388,42920,
%U A167214 47790,53320,59232,65604,72318,79660,87372,95608,104386,113646,123480
%N A167214 a(n) = (Sum of first n primes)*n
%F A167214 a(n)=n*A007504(n). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 31 2009]
%p A167214 A007504 := proc(n) add(ithprime(i),i=1..n) ; end: A167214 := proc(n) n*A007504(n) ; end: seq(A167214(n),n=1..80) ; [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 31 2009]
%p A167214 seq(n*add(ithprime(j), j = 1 .. n), n = 1 .. 40); [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 01 2009]
%K A167214 nonn,easy,new
%O A167214 1,1
%A A167214 Pratik Poddar (pratik(AT)cse.iitb.ac.in), Oct 30 2009
%E A167214 More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl) and Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 31 2009

%I A156037
%S A156037 1,1,4,6,10,12,16,18,22,28,30,36,40,42,46,52,58,60,66,70,72,78,82,88,96,
%T A156037 100,102,106,108,112,126,130,136,138,148,150,156,162,166,172,178,180,190,
%U A156037 192,196,198,210,222,226,228,232,238,240,250,256,262,268,270,276,280,282
%N A156037 Largest nonprime<nth prime.
%C A156037 Essentially the same as A006093.
%e A156037 a(1)=1 (1<2); a(2)=1 (1<3); a(3)=4 (4<5).
%p A156037 A156037 := proc(n) local a; for a from ithprime(n)-1 by -1 do if not isprime(a) then return a ; end if; end do: end proc: seq(A156037(n),n=1..80) ; # R. J. Mathar, Oct 30 2009
%Y A156037 Cf. A000040, A006093, A018252, A165972.
%K A156037 nonn,new
%O A156037 1,3
%A A156037 Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Oct 30 2009
%E A156037 166 inserted by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 31 2009

%I A167213
%S A167213 1,1,3,7,17,40,98,233,562,1349,3243,7789,18722,44978,108083,259700,
%T A167213 624027,1499427,3602913,8657216,20801982,49983920,120103675,288590527,
%U A167213 693438537,1666225599,4003682857,9620231375,23115930197,55544009564
%N A167213 The number of ordered ways to achieve a score of n in darts.
%C A167213 The game of darts has unmodified scores (1, 2, ..., 20), doubles of those values (2, 4, ..., 40), triples of those values (3, 6, ..., 60), and bull's eye values of 25 and 50.
%F A167213 G.f. = 1/(1-(x*(1-x^20)/(1-x)+x^2*(1-x^40)/(1-x^2)+x^3*(1-x^60)/(1-x^3)+x^25+x^50))
%e A167213 There are 7 ordered ways to get a total score of 3: (#1) "1","1","1"; (#2) "2","1"; (#3) "1","2"; (#4) "double 1","1" (#5) "1","double 1"; (#6) "triple 1"; and (#7) "3".
%K A167213 easy,nonn,new
%O A167213 0,3
%A A167213 Lee A. Newberg (integer(AT)quantconsulting.com), Oct 30 2009

%I A167211
%S A167211 1,2,3,4,5,6,7,8,11,13,15,16,17,19,21,23,29,31,32,33,37,39,40,41,43,47,
%T A167211 48,51,53,57,59,61,64,67,69,71,73,78,79,83,87,89,93,97
%N A167211 Numbers n such that number of perfect partitions of n divides n.
%Y A167211 Cf. A002033, A007694, A033950.
%K A167211 nonn,new
%O A167211 1,2
%A A167211 Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Oct 30 2009

%I A167210
%S A167210 0,15,30,40
%N A167210 Tennis scores: values of successive points in a game.
%C A167210 In English, 0 points is called "love." The fourth and higher points are not associated with numerical scores.
%C A167210 Originally "40" was "45". - njas, Oct 31 2009
%K A167210 easy,fini,full,nonn,new
%O A167210 0,2
%A A167210 Lee A. Newberg (integer(AT)quantconsulting.com), Oct 30 2009, Nov 02 2009

%I A167209
%S A167209 1,2,3,5,6,7,8,9,10,11,13,15,17,18,19,21,23,24,26,28,29,30,31,33,34,35,
%T A167209 37,39,40,41,43,45,47,49,51,52,53,55,56,58,59,61,63,65,67,69
%N A167209 d(n) divides phi(n).
%C A167209 Number of divisors of n divides Euler totient function phi(n).
%Y A167209 Cf. A000005, A000010, A000027.
%K A167209 nonn,new
%O A167209 1,2
%A A167209 Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Oct 30 2009

%I A167208
%S A167208 12,123,234,345,456,567,678,789,890,901,1012,1123,1234,1345,1456,1567,
%T A167208 1678,1789,1890,1901,2012,2123,2234,2345,2456,2567,2678,2789,2890,2901,
%U A167208 3012,3123,3234,3345,3456,3567,3678,3789,3890,3901,4012,4123
%N A167208 Append two digits, each increasing by one modulo 10 from the last digit the of the positive integers. 0 -> 12 1 -> 123 2 -> 234 .. 9 -> 901 10 -> 1012
%K A167208 base,easy,nonn,new
%O A167208 0,1
%A A167208 Felix Tubiana (fat2(AT)columbia.edu), Oct 30 2009

%I A167207
%S A167207 1,2,3,4,5,6,7,9,10,11,13,14,15,17,19,21,22,23,25,26,29,30,31,33,34,35,
%T A167207 37,38,39,41,42,43,46,47,49,51,53,55,57,58,59,61,62,65,66,67,69,70,71,
%U A167207 73,74,77,78,79,82,83,85,86,87,89,91,93,94,95,97,101,102,103,105,106
%N A167207 Numbers that are not divisible by a smaller number that is a square greater than 1
%e A167207 14 is included because there is no square strictly between 1 and 14 that divides evenly into 14.
%Y A167207 The union of A005117 (square-free numbers) and A001248 (squares of primes)
%K A167207 nonn,new
%O A167207 0,2
%A A167207 Lee A. Newberg (integer(AT)quantconsulting.com), Oct 30 2009

%I A167206
%S A167206 1,2,4,7,10,11,8,1,6,5,16,89,348,7747,58764,301959,1226902,4249557,
%T A167206 13125130,36998357,95306260,219609123,430081728,623477651,457458788,
%U A167206 3070156979,61496380490,630601717145,4635893019708,27904927526379
%V A167206 1,2,4,7,10,11,8,1,-6,-5,16,89,-348,-7747,-58764,-301959,-1226902,-4249557,
%W A167206 -13125130,-36998357,-95306260,-219609123,-430081728,-623477651,-457458788,
%X A167206 -3070156979,-61496380490,-630601717145,-4635893019708,-27904927526379
%N A167206 Binomial transform of A164555.
%C A167206 Binomial transform of the numerators of the Bernoulli number fractions A164555/A027642.
%p A167206 A164555 := proc(n) if n = 1 then -numer(bernoulli(n)) ; else numer(bernoulli(n)) ; end if; end proc:
%p A167206 read("transforms") : a164555 := [seq(A164555(n),n=0..50)] : BINOMIAL(a164555) ; # R. J. Mathar, Oct 31 2009
%Y A167206 Cf. A053223.
%K A167206 sign,new
%O A167206 0,2
%A A167206 Paul Curtz (bpcrtz(AT)free.fr), Oct 30 2009
%E A167206 Keyword:sign set, sequence extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 31 2009

%I A167200
%S A167200 6,10,14,18,2,30,34,38,26,46,62,66,70,42,78,54,94,126,130,134,74,142,50,
%T A167200 86,58,158,110,190,254
%N A167200 Multiply the A161924 by 4 then add 2,
%e A167200 a(n) begins 6 10 14 18 22 30 34 38 26 46 62 ...
%e A167200 because A161924 begins:
%e A167200 1.2.4..8.16.32.64.128.256.512.1024
%e A167200 ..3.5..9.17.33.65.129.257.513.1025
%e A167200 .......6.10.18.34..66.130.258..514
%e A167200 ....7.11.19.35.67.131.259.515.1027
%e A167200 ............12.20..36..68.132..260
%e A167200 .........13.21.37..69.133.261..517
%e A167200 ............14.22..38..70.134..262
%e A167200 ......15.23.39.71.135.263.519.1031
%e A167200 ...................24..40..72..136
%e A167200 ...............25..41..73.137..265
%e A167200 ...................26..42..74..138
%e A167200 ............27.43..75.139.267..523
%e A167200 .......................28..44...76
%e A167200 ...............29..45..77.141..269
%e A167200 ...................30..46..78..142
%e A167200 .........31.47.79.143.271.527.1039
%e A167200 ...........................48...80
%e A167200 .......................49..81..145
%e A167200 ...........................50...82
%e A167200 ...................51..83.147..275
%Y A167200 Cf. A000041 A161924
%K A167200 nonn,tabf,new
%O A167200 1,1
%A A167200 Alford Arnold (Alford1940(AT)aol.com), Oct 30 2009

%I A167205
%S A167205 1,1,5,7,41,61,365,547,3281,4921,29525,44287,265721,398581,2391485,
%T A167205 3587227,21523361,32285041,193710245,290565367,1743392201,2615088301,
%U A167205 15690529805,23535794707,141214768241,211822152361,1270932914165
%N A167205 (3^n+1)/(3-(-1)^n)
%F A167205 a(n)=10*a(n-2)-9*a(n-4)
%F A167205 G.f.: (1+x-5*x^2-3*x^3)/((1+x)*(1-x)*(1+3*x)*(1-3*x))
%Y A167205 Cf. A007051, A074476.
%K A167205 nonn,new
%O A167205 0,3
%A A167205 Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Oct 30 2009

%I A167198
%S A167198 1,1,2,1,2,3,1,4,2,3,5,1,4,6,2,7,3,5,8,1,9,4,6,10,2,7,11,3,12,5,8,13,1,
%T A167198 9,14,4,15,6,10,16,2,17,7,11,18,3,12,19,5,20,8,13,21,1,22,9,14,23,4,15,
%U A167198 24,6,25,10,16,26,2,17,27,7,28,11,18,29,3,30,12,19,31,5,20,32,8,33,13
%N A167198 Fractal sequence of the interspersion A083047.
%C A167198 As a fractal sequence, if the first occurrence of each term is deleted,
%C A167198 the remaining sequence is the original. In general, the interspersion
%C A167198 of a fractal sequence is constructed by rows: row r consists of all n,
%C A167198 such that a(n)=r; in particular, A083047 is constructed in this way
%C A167198 from A167198.
%F A167198 Following is a construction that avoids reference to A083047.
%F A167198 Write initial rows:
%F A167198 Row 1: .... 1
%F A167198 Row 2: .... 1
%F A167198 Row 3: .... 2..1
%F A167198 Row 4: .... 2..3..1
%F A167198 For n>=4, to form row n+1, let k be the least positive integer not yet
%F A167198 used; write row n, and right before the 1st number that is also in row n-1,
%F A167198 place k; right before the next number that is also in row n-1, place k+1,
%F A167198 and continue. A167198 is the concatenation of the rows. (If "before" is
%F A167198 replaced by "after", the resulting fractal sequence is A003603, and the
%F A167198 associated interspersion is the Wythoff array, A035513.)
%e A167198 To produce row 5, first write row 4: 2,3,1, then place 4 right before
%e A167198 2, and then place 5 right before 1, getting 4,2,3,5,1.
%Y A167198 Cf. A003603, A083047, A035513, A000045.
%K A167198 nonn,new
%O A167198 1,3
%A A167198 Clark Kimberling (ck6(AT)evansville.edu), Oct 30 2009

%I A167199
%S A167199 1,2,7,36,246,2100,21510,257040,3510360,53933040,920694600
%V A167199 1,-2,7,-36,246,-2100,21510,-257040,3510360,-53933040,920694600
%N A167199 First column of A167196.
%C A167199 Limiting ratio 2+n*a(n-1)/a(n) converges to A002193.
%Y A167199 Cf. A167196, A002193.
%K A167199 more,sign,new
%O A167199 0,2
%A A167199 Mats Granvik (mats.granvik(AT)abo.fi), Oct 30 2009

%I A167196
%S A167196 1,2,1,7,4,1,36,21,6,1,246,144,42,8,1,2100,1230,360,70,10,1,
%T A167196 21510,12600,3690,720,105,12,1,257040,150570,44100,8610,1260,147,
%U A167196 14,1,3510360,2056320,602280,117600,17220,2016,196,16,1,53933040
%V A167196 1,-2,1,7,-4,1,-36,21,-6,1,246,-144,42,-8,1,-2100,1230,-360,70,-10,1,
%W A167196 21510,-12600,3690,-720,105,-12,1,-257040,150570,-44100,8610,-1260,147,
%X A167196 -14,1,3510360,-2056320,602280,-117600,17220,-2016,196,-16,1,-53933040
%N A167196 Triangle T(n,k) read by rows: matrix inverse of A106246.
%C A167196 It appears that any square root can be calculated as a limiting ratio from the first column of the matrix inverse of a triangle similar to A106246. Replace the 2:s call them "x", in A167194 with an integer and multiply the A167194-like-triangle elementwise with the Pascal triangle A007318. Then divide the elements below the main diagonal in the resulting triangle with another integer.
%C A167196 For example x=3 so that the sequence in the columns is [1,3,1,0,0,0,0...]. The limiting ratio of the form n*a(n-1)/a(n) taken on the numbers in the first column of the matrix inverse will then converge to a square root of an integer - x. That is the square root = x+n*a(n-1)/a(n) where a(n) is the first column in the matrix inverse. The multiplying integer is related to the squares. The pattern of the dividing integer seems be every second square root downwards beginning minus two steps below the squareroot of the multiplying integer. The higher the dividing integer the lower the square root.
%C A167196 If instead as dividing number a fraction of the form [0,5;1,5;2,5;3,5;...] i.e. "a half, one and a half, two and a half ...", is chosen then the other every second square roots can be calculated. There is also a recursion such that if you instead of the 2:s in A167194 put a value of the previous every second square roots (either one of the every second square roots) you will get a square root that is two steps lower.
%C A167196 Contribution from Mats Granvik (mats.granvik(AT)abo.fi), Oct 31 2009: (Start)
%C A167196 To calculate the square root of x consider the triangle A:
%C A167196 1,
%C A167196 x,1,
%C A167196 1,x,1,
%C A167196 0,1,x,1,
%C A167196 0,0,1,x,1,
%C A167196 0,0,0,1,x,1,
%C A167196 0,0,0,0,1,x,1,
%C A167196 0,0,0,0,0,1,x,1
%C A167196 Define y=(x-1)*x/2 and consider the triangle B:
%C A167196 1,
%C A167196 y,1,
%C A167196 y,y,1,
%C A167196 y,y,y,1,
%C A167196 y,y,y,y,1,
%C A167196 y,y,y,y,y,1,
%C A167196 y,y,y,y,y,y,1,
%C A167196 y,y,y,y,y,y,y,1
%C A167196 Consider the Pascal triangle:
%C A167196 1
%C A167196 1..1
%C A167196 1..2..1
%C A167196 1..3..3..1
%C A167196 1..4..6..4..1
%C A167196 1..5.10.10..5..1
%C A167196 1..6.15.20.15..6..1
%C A167196 1..7.21.35.35.21..7..1
%C A167196 Multiply the elements in the Pascal triangle with the elements in triangle A and divide with the elements in triangle B so that you get:
%C A167196 1*1/1
%C A167196 1*x/y...1*1/1
%C A167196 1*1/y...2*x/y...1*1/1
%C A167196 ....0...3*1/y...3*x/y.....1*1/1
%C A167196 ....0.......0...6*1/y.....4*x/y...1*1/1
%C A167196 ....0.......0.......0....10*1/y...5*x/y...1*1/1
%C A167196 ....0.......0.......0.........0..15*1/y...6*x/y...1*1/1
%C A167196 ....0.......0.......0.........0.......0..21*1/y...7*x/y...1*1/1
%C A167196 which when simplified becomes triangle D:
%C A167196 ..1
%C A167196 x/y.......1
%C A167196 1/y...2*x/y.......1
%C A167196 ..0.....3/y...3*x/y.........1
%C A167196 ..0.......0.....6/y.....4*x/y.......1
%C A167196 ..0.......0.......0......10/y...5*x/y.......1
%C A167196 ..0.......0.......0.........0....15/y...6*x/y.......1
%C A167196 ..0.......0.......0.........0.......0....21/y...7*x/y.......1
%C A167196 Calculate the matrix inverse of triangle D. In the case of x=2 the matrix inverse of triangle D is this triangle A167196. The ratio of the form: x+n*a(n-1)/a(n) appears to converge to sqrt(x) as n-->infinity. See A167199 for example. (End)
%e A167196 Contribution from Mats Granvik (mats.granvik(AT)abo.fi), Oct 31 2009: (Start)
%e A167196 Table begins:
%e A167196 ......1
%e A167196 .....-2.......1
%e A167196 ......7......-4.......1
%e A167196 ....-36......21......-6.......1
%e A167196 ....246....-144......42......-8.......1
%e A167196 ..-2100....1230....-360......70.....-10.......1
%e A167196 ..21510..-12600....3690....-720.....105.....-12.......1
%e A167196 -257040..150570..-44100....8610...-1260.....147.....-14.......1
%e A167196 (End)
%Y A167196 Cf. A106246.
%Y A167196 Cf. A167199. [From Mats Granvik (mats.granvik(AT)abo.fi), Oct 31 2009]
%K A167196 sign,tabl,new
%O A167196 1,2
%A A167196 Mats Granvik, Roger L. Bagula, Gary W. Adamson, Paul Barry. (mats.granvik(AT)abo.fi), Oct 30 2009

%I A156034
%S A156034 1,1,2,1,6,8,80,45,280,896,145152,100800,13305600,68428800,7907328,90810720,
%T A156034 326918592000,258306048000,79041650688000,64023737057280,55167845990400,
%U A156034 10532043325440000,9289262213038080000,7805560609566720000,6893871130369327104
%N A156034 Denominator of (Sum_{k=1..n} k^3)/n!.
%Y A156034 See A156033 for further information.
%K A156034 nonn,frac,new
%O A156034 0,3
%A A156034 N. J. A. Sloane (njas(AT)research.att.com), Oct 31 2009

%I A156033
%S A156033 0,1,9,6,25,15,49,7,9,5,121,11,169,91,1,1,289,17,361,19,1,11,529,23,1,13,
%T A156033 1,1,841,29,961,31,1,17,1,1,1369,703,1,1,1681,41,1849,43,1,23,2209,47,1,
%U A156033 1,1,1,2809,53,1,1,1,29,3481,59,3721,1891,1,1,1,1,4489,67,1,1,5041,71,5329
%N A156033 Numerator of (Sum_{k=1..n} k^3)/n!.
%D A156033 V. Mangulis, Handbook of Series, Academic Press, 1965, p. 77.
%F A156033 Sum_{ n>=1 } x^n*(Sum_{k=1..n} k^3)/n! = x*exp(x)*(x^3+8*x^2+14*x+4)/4.
%e A156033 0, 1, 9/2, 6, 25/6, 15/8, 49/80, 7/45, 9/280, 5/896, 121/145152, 11/100800, 169/13305600, ...
%Y A156033 Cf. A156034.
%K A156033 nonn,frac,new
%O A156033 0,3
%A A156033 N. J. A. Sloane (njas(AT)research.att.com), Oct 31 2009

%I A156032
%S A156032 1,360,302400,122594472000,333456963840000,7840406862288000000,4962375400581280281600000,
%T A156032 32379499488792853837440000000,32762872762740161226875289600000000,49021399349801594985745916351847936000000000,
%U A156032 210558581969147803224489602616032563200000000000,874618237783446145033884911346476061020160000000000
%N A156032 Denominators to accompany A156036.
%K A156032 nonn,frac,new
%O A156032 0,2
%A A156032 N. J. A. Sloane (njas(AT)research.att.com), Oct 31 2009

%I A156036
%S A156036 0,1,1,691,3617,174611,236364091,3392780147,7709321041217,26315271553053477373,
%T A156036 261082718496449122051,2530297234481911294093,5609403368997817686249127547,
%U A156036 61628132164268458257532691681,354198989901889536240773677094747,1215233140483755572040304994079820246041491
%V A156036 0,-1,1,-691,3617,-174611,236364091,-3392780147,7709321041217,-26315271553053477373,
%W A156036 261082718496449122051,-2530297234481911294093,5609403368997817686249127547,
%X A156036 -61628132164268458257532691681,354198989901889536240773677094747,-1215233140483755572040304994079820246041491
%N A156036 Numerators in expansion of log(z^2/(cosh(z)-cos(z))).
%D A156036 V. Mangulis, Handbook of Series, Academic Press, 1965, p. 76.
%F A156036 log(z^2/(cosh(z)-cos(z))) = Sum_{ n >= 1 } (-1)^n*B_{2n}*(2z^2)^(2n)/((4n)!2n).
%e A156036 log(z^2/(cosh(z)-cos(z))) = -(1/360)*z^4+(1/302400)*z^8-(691/122594472000)*z^12+(3617/333456963840000)*z^16+...
%Y A156036 Cf. A156032.
%K A156036 sign,frac,new
%O A156036 0,4
%A A156036 N. J. A. Sloane (njas(AT)research.att.com), Oct 31 2009

%I A167194
%S A167194 1,2,1,1,2,1,0,1,2,1,0,0,1,2,1,0,0,0,1,2,1,0,0,0,0,1,2,1,0,0,0,0,0,1,2,
%T A167194 1,0,0,0,0,0,0,1,2,1,0,0,0,0,0,0,0,1,2,1,0,0,0,0,0,0,0,0,1,2,1,0,0,0,0,
%U A167194 0,0,0,0,0,1,2,1,0,0,0,0,0,0,0,0,0,0,1,2,1
%N A167194 Triangle read by rows. A130713 in the columns.
%e A167194 Table begins:
%e A167194 1,
%e A167194 2,1,
%e A167194 1,2,1,
%e A167194 0,1,2,1,
%e A167194 0,0,1,2,1,
%e A167194 0,0,0,1,2,1,
%e A167194 0,0,0,0,1,2,1,
%e A167194 0,0,0,0,0,1,2,1,
%e A167194 0,0,0,0,0,0,1,2,1,
%e A167194 0,0,0,0,0,0,0,1,2,1,
%e A167194 0,0,0,0,0,0,0,0,1,2,1,
%Y A167194 Cf. A130713.
%K A167194 nonn,tabl,new
%O A167194 1,2
%A A167194 Mats Granvik (mats.granvik(AT)abo.fi), Oct 30 2009

%I A167197
%S A167197 7,14,16,17,18,19,20,21,28,29,30,31,32,33,34,35,36,37,38,39,52,53,54,55,
%T A167197 60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,
%U A167197 83,84,85,86,87,116
%N A167197 a(6)=7, for n>=7, a(n)=a(n-1)+gcd(n, a(n-1))
%C A167197 For every n>=7, a(n)-a(n-1) is 1 or prime. This Roland-like "generator of primes" is different from A106108 (see comment to A167168) and from A167170. Note that, lim sup a(n)/n=2, while lim sup A106108(n)/n=lim sup A167170(n)/n=3.
%D A167197 E. S. Rowland, A natural prime-generating recurrence , Journal of Integer Sequences, Vol.11(2008), Article 08.2.8
%H A167197 V.Shevelev, <a href="http://arXiv.org/abs/math.0910.4676">A new generator of primes based on the Rowland idea</a>
%Y A167197 A167195 A167170 A167168 A106108 A132199 A167054 A167053 A166944 A166945 A163960 A163961 A163963 A084662 A084663 A134162 A135506 A135508 A118679 A120293
%K A167197 nonn,uned,new
%O A167197 6,1
%A A167197 Vladimir Shevelev (shevelev(AT)bgu.ac.il), Oct 30 2009

%I A167195
%S A167195 3,6,8,9,12,13,14,15,20,21,24,25,26,27,28,29,30,31,32,33,44,45,48,49,50,
%T A167195 51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,92,93,96,97,98,
%U A167195 99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116
%N A167195 a(2)=3, for n>=3, a(n)=a(n-1)+gcd(n, a(n-1))
%C A167195 For every n>=3, a(n)-a(n-1) is 1 or prime. This Roland-like "generator of primes" is different from A106108 and from generators A167168. Generalization: Let p be a prime. Let N(p-1)=p and for n>=p, N(n)=N(n-1)+gcd(n, N(n-1)). Then, for every n>=p, N(n)-N(n-1) is 1 or prime.
%H A167195 E. S. Rowland, A natural prime-generating recurrence, <a href="http://www.cs.uwaterloo.ca/journals/JIS/vol11.html">Journal of Integer Sequences 11</a> (2008), Article 08.2.8
%H A167195 V.Shevelev, <a href="http://arXiv.org/abs/math.0910.4676">A new generator of primes based on the Rowland idea</a>
%Y A167195 A167170 A167168 A106108 A132199 A167054 A167053 A166944 A166945 A163960 A163961 A163963 A084662 A084663 A134162 A135506 A135508 A118679 A120293
%K A167195 nonn,easy,new
%O A167195 2,1
%A A167195 Vladimir Shevelev (shevelev(AT)bgu.ac.il), Oct 30 2009
%E A167195 Edited by Charles R Greathouse IV (charles.greathouse(AT)case.edu), Nov 02 2009

%I A167191
%S A167191 2664,20568,68592,161616,314520,542184
%N A167191 Kindy see previous seq: A167190 for description.
%e A167191 Already illustrated in previous sequence (cf. A167190).
%Y A167191 A165806, A165808, A165809, A166957, A167190
%K A167191 nonn,uned,new
%O A167191 1,1
%A A167191 A.K.Devaraj (dkandadai(AT)gmail.com), Oct 30 2009

%I A167193
%S A167193 1,0,0,2,4,10,20,42,84,170,340,682,1364
%V A167193 1,0,0,2,-4,10,-20,42,-84,170,-340,682,-1364
%N A167193 Inverse binomial transform of 1,A001045= A152046 ? Mix A084240 signed , A020988.
%C A167193 In A167167 read A152046 instead of A152406;also in A090129.
%F A167193 A167130 signed. a(n)=-a(n-1)+2a(n-2)-2*(-1)^n; a(n)=-2a(n-1)+a(n-2)+2a(n-3) ,a(0)=1,a(1)=a(2)=0; a(n)=5a(n-2)-4a(n-4).See A101622.
%K A167193 nonn,uned,new
%O A167193 0,4
%A A167193 Paul Curtz (bpcrtz(AT)free.fr), Oct 30 2009

%I A167190
%S A167190 17594,131307,432796,1013717,1965726,3380479
%N A167190 As mentioned in the short description of the recently published sequence (A166957) polynomials in two variables, not necessarily homogeneous, also have a property similar to that in a single variable (cf. A165806, A165808 and A165809) viz f(x+k*f(x,y), y + k*f(x,y)) is congruent to 0 (mod(f(x,y)). The quotient has two parts: a rational integer and a rational integer coefficient of sqrt(-1), when x belongs to Z(x = 5) and y is complex (sqrt(-1)). The polynomial considered is identical with that in A166957 viz x^3 + 2xy + y^2. The present sequence is only that of the rational integers and seq A167191 will consist of rational integer coeffficients of sqrt(-1).Note: k belongs to N.
%e A167190 When x = 5 and y = i f(x,y) = x^3 + 2xy + y^2 = 124 + 10i. The quotient of f(x + f(x,y), y + f(x,y))/(124 + 10i) is 17594 + 2664i.
%p A167190 Although no program in pari has been used the pari calculator was used. Needless to say the division was rendered after rationalisation of the denominator.
%Y A167190 Cf. A165806, A165808, A165809 & A 166957.
%K A167190 nonn,uned,new
%O A167190 1,1
%A A167190 A.K.Devaraj (dkandadai(AT)gmail.com), Oct 30 2009

%I A167192
%S A167192 0,1,0,2,1,0,3,1,1,0,4,3,2,1,0,5,2,1,1,1,0,6,5,4,3,2,1,0,7,3,5,1,3,1,1,
%T A167192 0,8,7,2,5,4,1,2,1,0,9,4,7,3,1,2,3,1,1,0,10,9,8,7,6,5,4,3,2,1,0,11,5,3,
%U A167192 2,7,1,5,1,1,1,1,0,12,11,10,9,8,7,6,5,4,3,2,1,0,13,6,11,5,9,4,1,3,5,2,3
%N A167192 Triangle read by rows: T(n,k) = (n-k)/GCD(n,k), 1<=k<=n.
%C A167192 T(n,k) = A025581(n,k)/A050873(n,k);
%C A167192 T(n,1) = A001477(n-1);
%C A167192 T(n,2) = A026741(n-2) for n>1;
%C A167192 T(n,3) = A051176(n-3) for n>2;
%C A167192 T(n,4) = A060819(n-4) for n>4;
%C A167192 T(n,n-3) = A144437(n) for n>3;
%C A167192 T(n,n-2) = A000034(n) for n>2;
%C A167192 T(n,n-1) = A000012(n);
%C A167192 T(n,n) = A000004(n).
%Y A167192 A164306, A054531.
%K A167192 nonn,tabl,new
%O A167192 1,4
%A A167192 Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 30 2009

%I A167186
%S A167186 3,4,7,9,17,40,41,74,151,307,312,408,424,912,1032,1217,1872,2518,3713,
%T A167186 4920,5208,8400,8520,8892,9297,12840,16008,21840,24360,35880,38808,
%U A167186 80760,102168,129480,167160,183960,201072,258720,290760,301242,358848
%N A167186 Record gaps between non-prime prime powers.
%e A167186 17 is in the sequence since A025475(9) - A025475(8) = 49 - 32 = 17, and no previous gap is larger.
%e A167186 A025475(10) - A025475(9) = 64 - 49 = 15, but the previous gap is larger, so 15 is not in the sequence.
%o A167186 (PARI) isA025475(n) = (omega(n) == 1 & !isprime(n)) | (n == 1)
%o A167186 d_max=0;n_prev=1;for(n=2,32e6,if(isA025475(n),d=n-n_prev;n_prev=n;if(d>d_max,print(d);d_max=d)))
%Y A167186 List of non-prime prime powers: A025475
%Y A167186 Gaps between non-prime prime powers: A053707
%Y A167186 Record gaps between prime powers including primes: A167235
%K A167186 nonn,new
%O A167186 1,1
%A A167186 Michael Porter (michael_b_porter(AT)yahoo.com), Oct 29 2009, Oct 31 2009

%I A167185
%S A167185 1,1,1,4,4,4,4,8,9,9,9,9,9,9,9,16,16,16,16,16,16,16,16,16,25,25,27,27,
%T A167185 27,27,27,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,49,49,49,
%U A167185 49,49,49,49,49,49,49,49,49,49,49,49,64,64,64,64,64,64,64,64,64,64,64
%N A167185 Largest prime power <= n that is not prime.
%e A167185 For a(14), 10, 12, and 14 are not prime powers, and 11 and 13 are prime powers but they are prime. Since 9 = 3^3 is a prime power, a(14) = 9.
%o A167185 (PARI) isA025475(n) = (omega(n) == 1 & !isprime(n)) | (n == 1)
%o A167185 A167185(n) = {local(m);m=n;while(!isA025475(m),m--);m}
%Y A167185 List of non-prime prime powers: A025475
%Y A167185 Next non-prime prime power: A167184
%Y A167185 Previous prime power including primes: A031218
%K A167185 easy,nonn,new
%O A167185 1,4
%A A167185 Michael Porter (michael_b_porter(AT)yahoo.com), Oct 29 2009

%I A167184
%S A167184 1,4,4,4,8,8,8,8,9,16,16,16,16,16,16,16,25,25,25,25,25,25,25,25,25,27,
%T A167184 27,32,32,32,32,32,49,49,49,49,49,49,49,49,49,49,49,49,49,49,49,49,49,
%U A167184 64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,81,81,81,81,81,81,81,81
%N A167184 Smallest prime power >= n that is not prime.
%e A167184 For a(12), 12, 14, and 15 are not prime powers, and 13 is a prime power but it is prime. Since 16 = 2^4 is a prime power, a(12) = 16.
%o A167184 (PARI) isA025475(n) = (omega(n) == 1 & !isprime(n)) | (n == 1)
%o A167184 A167184(n) = {local(m);m=n;while(!isA025475(m),m++);m}
%Y A167184 List of non-prime prime powers: A025475
%Y A167184 Previous non-prime prime power: A167185
%Y A167184 Next prime power including primes: A000015
%K A167184 easy,nonn,new
%O A167184 1,2
%A A167184 Michael Porter (michael_b_porter(AT)yahoo.com), Oct 29 2009

%I A166297
%S A166297 0,0,0,1,2,5,12,28,66,156,370,882,2112,5079,12264,29725,72298,176414,
%T A166297 431754,1059595,2607090,6429913,15893330,39365876,97692372,242875105,
%U A166297 604836072,1508619585,3768496102,9426815859,23612178180,59217406914
%N A166297 Number of UUDUDD's starting at level 0 in all Dyck paths of semilength n with no UUU's and no DDD's (U=(1,1), D=(1,-1)).
%C A166297 a(n)=Sum(k*A166295(n,k), k=0..floor(n/3)).
%F A166297 G.f.: G(z)=4z^3/(1-z-z^2+sqrt(1-2*z-z^2-2*z^3+z^4))^2.
%e A166297 a(3)=1 because in UDUDUD, UDUUDD, UUDDUD, and UUDUDD we have 0+0+0+1=1 UUDUDD's starting at level 0.
%p A166297 G := 4*z^3/(1-z-z^2+sqrt(1-2*z-z^2-2*z^3+z^4))^2: Gser := series(G, z = 0, 35): seq(coeff(Gser, z, n), n = 0 .. 32);
%Y A166297 A166295
%K A166297 nonn,new
%O A166297 0,5
%A A166297 Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 29 2009

%I A166296
%S A166296 1,1,2,3,6,12,26,57,128,291,670,1558,3655,8639,20554,49185,118301,
%T A166296 285840,693480,1688683,4125882,10111393,24849532,61226546,151212789,
%U A166296 374271925,928254590,2306569185,5741561804,14315544330,35748249574
%N A166296 Number of Dyck paths of semilength n with no UUU's and no DDD's and having no UUDUDD's starting at level 0 (U=(1,1), D=(1,-1)).
%C A166296 a(n)=A166295(n,0).
%F A166296 G.f.: G=2/[1-z-z^2+2*z^3+sqrt(1-2z-z^2-2z^3+z^4)].
%e A166296 a(3)=3 because we have UDUDUD, UDUUDD, and UUDDUD.
%p A166296 G := 2/(1-z-z^2+2*z^3+sqrt(1-2*z-z^2-2*z^3+z^4)): Gser := series(G, z = 0, 35): seq(coeff(Gser, z, n), n = 0 .. 32);
%Y A166296 A166295
%K A166296 nonn,new
%O A166296 0,3
%A A166296 Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 29 2009

%I A166295
%S A166295 1,1,2,3,1,6,2,12,5,26,10,1,57,22,3,128,48,9,291,109,22,1,670,250,54,4,
%T A166295 1558,582,129,14,3655,1366,311,40,1,8639,3232,750,109,5,20554,7696,1818,
%U A166295 284,20,49185,18432,4419,730,65,1,118301,44368,10776,1856,195,6
%N A166295 Triangle read by rows: T(n,k) is the number of Dyck paths with no UUU's and no DDD's, of semilength n and having k UUDUDD's starting at level 0 (0<=k<=floor(n/3); U=(1,1), D=(1,-1)).
%C A166295 Row n has 1+floor(n/3) terms.
%C A166295 Sum of entries in row n = A004148(n+1) (the secondary structure numbers).
%C A166295 T(n,0)=A166296(n).
%C A166295 Sum(k*T(n,k), k=0..floor(n/3))=A166297(n).
%F A166295 G.f.: G(t,z) = 1/(1-z-z^2+z^3-t*z^3-z^3*g), where g = 1+zg + z^2*g + z^3*g^2.
%e A166295 T(4,1)=2 because we have UDUUDUDD and UUDUDDUD.
%e A166295 Triangle starts:
%e A166295 1;
%e A166295 1;
%e A166295 2;
%e A166295 3, 1;
%e A166295 6, 2;
%e A166295 12, 5;
%e A166295 26, 10, 1;
%p A166295 G := 2/(1-z-z^2+2*z^3-2*t*z^3+sqrt(1-2*z-z^2-2*z^3+z^4)): Gser := simplify(series(G, z = 0, 20)): for n from 0 to 16 do P[n] := sort(coeff(Gser, z, n)) end do: for n from 0 to 16 do seq(coeff(P[n], t, j), j = 0 .. floor((1/3)*n)) end do; # yields sequence in triangular form
%Y A166295 A004148, A166296, A166297
%K A166295 nonn,tabf,new
%O A166295 0,3
%A A166295 Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 29 2009

%I A167187
%S A167187 73,719,743,761,773,797,7103,7109,7127,7151,7193,7211,7229,7283,7331,
%T A167187 7349,7433,7457,7487,7499,7523,7541,7547,7577,7607,7643,7673,7691,7727,
%U A167187 7757,7823,7829,7853,7877,7883,7907,7919,7937,71039,71069,71129,71153
%N A167187 Primes obtained from other primes by prefixing a 7.
%C A167187 The primes are considered in increasing order.
%e A167187 7151 is a prime obtained by prefixing a 7 to the prime 151.
%Y A167187 Cf. A000040, A165243, A165292, A165444
%K A167187 base,nonn,new
%O A167187 1,1
%A A167187 Parthasarathy Nambi (PachaNambi(AT)yahoo.com), Oct 29 2009
%E A167187 More terms (a(11)-a(42) from Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 01 2009

%I A166298
%S A166298 0,0,0,0,2,19,140,956,6506,45659,336996,2643979,22160244,198618081,
%T A166298 1901082872,19381817300,209829985306,2404750030651,29088407474132,
%U A166298 370369420974335,4951491489003676,69348849926870881,1015423795024288712
%N A166298 Number of simsun permutations of {1,2,...,n} having at least one 321 pattern. A permutation p in S_n is said to be simsun if it has no double descents and with the hereditary property that when n, n-1, ..., 2, 1 are deleted in succession, the property of not having double descents is preserved after each deletion.
%F A166298 a(n)=E(n+1) - C(n), where E(k) are the Euler (or up-down numbers; A000111(k)) and C(k) are the Catalan numbers (A000108(k)).
%e A166298 a(4)=2 because we have 4132 and 4231 (the other C(4)=14 simsun permutations of {1,2,3,4} have no 321 patterns at all).
%p A166298 f := sec(x)+tan(x): fser := series(f, x = 0, 52): E := proc (n) options operator, arrow: factorial(n)*coeff(fser, x, n) end proc: C := proc (n) options operator, arrow: binomial(2*n, n)/(n+1) end proc: seq(E(n+1)-C(n), n = 0 .. 23);
%Y A166298 Cf. A000111, A000108
%K A166298 nonn,new
%O A166298 0,5
%A A166298 Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 29 2009

%I A167180
%S A167180 1,2,4,5,9,10,14,15,18,23,25,30,34,35,38,43,49,50,56,59,60,65,69,74,81,
%T A167180 84,85,89,90,94,107,110,115,116,125,127,132,137,140,146,151,153,162,163,
%U A167180 166,168,179,190,193,194,197,203,204,213,218,223,228,230,235
%N A167180 a(n) = pi(n) plus the number of nonprimes less than prime(n).
%C A167180 The number of primes less than n plus number of nonprimes less than nth prime.
%F A167180 a(n)=A000720(n)+A014689(n).
%Y A167180 Cf. A000027, A000040, A000720, A014689, A018252.
%K A167180 nonn,new
%O A167180 1,2
%A A167180 Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Oct 29 2009

%I A156030
%S A156030 1,0,1,3,5,7,3,4,9,4,7,9,4,7,2,2,2,1,5,8,5,6,0,1,1,5,7,0,9,3,0,2,7,1,9,
%T A156030 7,6,3,9,6,7,1,7,1,6,3,5,4,4,8,0,8,3,0,4,0,7,8,3,0,3,3,7,3,6,2,8,7,9,2,
%U A156030 2,7,7,1,3,6,8,4,4,1,9,6,7,3,4,4,3,0,7,7,1,6,0,7,4,8,9,5,1
%N A156030 Decimal expansion of log_23 (24).
%e A156030 1.0135734947947222158560115709302719763967171635448083040783...
%K A156030 nonn,cons,new
%O A156030 1,4
%A A156030 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A156029
%S A156029 1,0,2,8,1,4,9,5,2,5,0,5,5,8,9,0,0,5,0,9,1,2,9,7,3,0,8,5,9,9,2,6,0,5,8,
%T A156029 0,0,2,1,3,9,1,6,9,8,9,1,5,7,8,8,2,7,6,5,4,8,3,4,9,8,3,6,1,0,8,6,0,0,2,
%U A156029 3,0,8,0,5,1,2,9,7,3,8,3,1,2,8,3,4,4,1,2,2,5,4,7,2,2,6,2,3
%N A156029 Decimal expansion of log_22 (24).
%e A156029 1.0281495250558900509129730859926058002139169891578827654834...
%K A156029 nonn,cons,new
%O A156029 1,3
%A A156029 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A156028
%S A156028 1,0,4,3,8,5,9,5,5,2,8,0,5,3,8,9,1,6,7,1,9,1,3,1,1,7,1,2,8,0,6,9,7,8,2,
%T A156028 4,6,9,8,7,5,8,3,2,5,3,4,7,2,7,2,7,5,3,6,1,6,0,8,1,3,0,0,7,2,0,8,2,9,6,
%U A156028 0,0,0,9,5,1,8,4,0,2,8,1,6,4,9,0,4,6,5,3,3,4,4,7,2,9,5,5,1
%N A156028 Decimal expansion of log_21 (24).
%e A156028 1.0438595528053891671913117128069782469875832534727275361608...
%K A156028 nonn,cons,new
%O A156028 1,3
%A A156028 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A156015
%S A156015 1,0,6,0,8,6,0,4,3,0,8,2,1,3,6,2,1,5,1,7,0,3,9,0,0,2,4,5,9,5,2,2,5,4,1,
%T A156015 4,1,2,6,8,6,6,4,9,5,3,0,5,3,0,2,9,6,5,3,8,0,7,8,4,0,9,5,9,6,1,5,5,2,0,
%U A156015 3,5,9,0,2,2,0,4,4,2,6,3,5,2,0,7,0,2,6,8,9,9,1,8,6,6,8,1,9
%N A156015 Decimal expansion of log_20 (24).
%e A156015 1.0608604308213621517039002459522541412686649530530296538078...
%K A156015 nonn,cons,new
%O A156015 1,3
%A A156015 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A156000
%S A156000 1,0,7,9,3,4,1,0,4,0,1,2,1,5,5,1,6,5,8,2,1,9,1,2,8,7,4,8,2,1,5,7,1,8,5,
%T A156000 9,7,7,3,1,8,3,7,0,7,8,1,3,5,5,8,4,4,9,9,8,5,3,2,6,3,3,4,7,4,5,5,4,5,2,
%U A156000 0,9,8,1,1,9,2,1,0,7,6,2,2,8,1,3,5,0,1,8,7,5,4,1,0,4,1,0,7
%N A156000 Decimal expansion of log_19 (24).
%e A156000 1.0793410401215516582191287482157185977318370781355844998532...
%K A156000 nonn,cons,new
%O A156000 1,3
%A A156000 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155995
%S A155995 1,0,9,9,5,3,1,1,6,6,4,2,0,3,2,8,6,1,1,8,3,9,2,1,0,4,1,2,2,7,6,3,0,7,6,
%T A155995 5,4,4,2,0,4,4,4,8,2,5,0,4,7,6,7,6,4,1,4,9,4,6,6,1,2,2,5,1,7,8,7,2,8,2,
%U A155995 2,6,4,3,5,7,9,7,3,8,6,2,1,2,6,6,3,9,1,0,3,7,0,0,3,5,2,8,1
%N A155995 Decimal expansion of log_18 (24).
%e A155995 1.0995311664203286118392104122763076544204448250476764149466...
%K A155995 nonn,cons,new
%O A155995 1,3
%A A155995 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155992
%S A155992 1,1,2,1,7,1,3,5,6,1,3,9,3,1,6,8,1,6,6,6,0,5,4,8,3,8,3,4,4,3,0,3,5,2,0,
%T A155992 6,9,0,1,3,4,5,6,5,2,6,2,6,8,9,6,7,3,3,5,7,0,5,8,0,9,3,9,2,8,7,2,4,0,1,
%U A155992 2,4,6,2,6,4,5,1,1,1,1,4,9,0,2,2,2,0,3,8,3,6,1,2,2,8,2,3,3
%N A155992 Decimal expansion of log_17 (24).
%e A155992 1.1217135613931681666054838344303520690134565262689673357058...
%K A155992 nonn,cons,new
%O A155992 1,3
%A A155992 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155991
%S A155991 1,1,4,6,2,4,0,6,2,5,1,8,0,2,8,9,0,4,5,3,6,3,4,3,4,7,3,5,9,8,6,9,5,4,1,
%T A155991 2,7,1,8,9,9,5,3,6,0,1,9,2,3,1,2,0,2,6,5,1,1,3,9,3,8,1,6,3,6,3,5,2,7,4,
%U A155991 5,5,6,9,4,8,5,8,9,6,4,0,6,3,0,5,7,0,1,1,8,7,2,9,5,2,2,0,6
%N A155991 Decimal expansion of log_16 (24).
%e A155991 1.1462406251802890453634347359869541271899536019231202651139...
%K A155991 nonn,cons,new
%O A155991 1,3
%A A155991 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155987
%S A155987 1,1,7,3,5,5,7,9,4,5,5,1,1,6,5,9,3,6,2,5,4,5,9,3,8,0,3,3,1,9,5,7,9,9,3,
%T A155987 4,0,7,1,4,6,9,3,4,1,7,5,4,2,9,8,3,8,5,4,2,3,1,8,9,3,3,1,8,9,7,0,0,2,8,
%U A155987 8,3,2,6,0,5,5,9,0,2,7,9,9,2,4,7,9,7,5,4,2,6,7,2,4,1,2,6,4
%N A155987 Decimal expansion of log_15 (24).
%e A155987 1.1735579455116593625459380331957993407146934175429838542318...
%K A155987 nonn,cons,new
%O A155987 1,3
%A A155987 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155984
%S A155984 1,2,0,4,2,3,8,2,6,8,9,7,7,3,7,9,8,5,8,4,7,3,2,6,1,2,9,8,0,3,7,7,9,3,8,
%T A155984 9,0,7,8,8,7,8,3,7,7,7,8,4,5,1,7,5,3,4,6,4,2,2,5,3,3,9,3,5,9,8,7,1,8,7,
%U A155984 8,9,5,1,6,9,6,6,2,5,2,2,7,6,0,7,8,6,1,6,6,0,5,6,1,7,0,6,4
%N A155984 Decimal expansion of log_14 (24).
%e A155984 1.2042382689773798584732612980377938907887837778451753464225...
%K A155984 nonn,cons,new
%O A155984 1,2
%A A155984 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155983
%S A155983 1,2,3,9,0,3,1,8,0,4,3,1,3,3,5,3,9,0,4,8,7,3,0,9,8,3,8,8,2,7,2,8,9,1,4,
%T A155983 6,0,1,0,2,5,6,3,5,3,5,3,2,4,7,2,8,0,6,5,2,0,8,1,6,8,0,1,1,0,1,0,3,0,9,
%U A155983 2,0,3,7,2,6,7,6,2,8,9,8,1,0,7,9,8,5,2,1,6,9,3,9,0,5,7,3,0
%N A155983 Decimal expansion of log_13 (24).
%e A155983 1.2390318043133539048730983882728914601025635353247280652081...
%K A155983 nonn,cons,new
%O A155983 1,2
%A A155983 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155982
%S A155982 1,2,7,8,9,4,2,9,4,5,6,5,1,1,2,9,8,4,3,1,9,1,0,4,4,0,8,1,0,3,7,8,8,5,6,
%T A155982 0,3,1,0,4,7,9,4,3,3,7,5,9,6,4,7,3,0,6,7,9,7,2,6,9,6,0,0,3,4,0,8,2,7,6,
%U A155982 5,0,5,2,4,0,4,6,7,5,5,9,0,8,0,6,9,7,2,1,7,3,5,0,3,6,3,1,1
%N A155982 Decimal expansion of log_12 (24).
%e A155982 1.2789429456511298431910440810378856031047943375964730679726...
%K A155982 nonn,cons,new
%O A155982 1,2
%A A155982 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155981
%S A155981 1,3,2,5,3,5,1,3,8,8,9,4,4,9,8,9,8,0,0,2,8,0,8,5,1,2,5,6,9,9,3,5,4,3,3,
%T A155981 1,7,4,9,8,5,0,3,2,3,3,5,8,1,9,0,5,3,3,9,5,4,1,3,4,4,1,7,5,6,2,2,8,9,3,
%U A155981 5,5,3,2,9,5,2,5,8,5,8,0,2,4,3,3,8,7,3,2,3,1,0,2,1,7,8,9,6
%N A155981 Decimal expansion of log_11 (24).
%e A155981 1.3253513889449898002808512569935433174985032335819053395413...
%K A155981 nonn,cons,new
%O A155981 1,2
%A A155981 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155979
%S A155979 1,3,8,0,2,1,1,2,4,1,7,1,1,6,0,6,0,2,2,9,3,6,2,4,4,5,8,7,4,2,8,5,9,4,3,
%T A155979 8,9,5,0,4,6,9,8,5,0,8,5,7,7,0,2,1,4,8,8,7,6,1,1,4,8,0,2,3,6,8,6,5,5,3,
%U A155979 7,2,0,6,0,6,9,3,4,6,5,1,5,0,3,7,5,0,1,1,2,0,0,2,1,7,4,8,1
%N A155979 Decimal expansion of log_10 (24).
%e A155979 1.3802112417116060229362445874285943895046985085770214887611...
%K A155979 nonn,cons,new
%O A155979 1,2
%A A155979 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155976
%S A155976 1,4,4,6,3,9,4,6,3,0,3,5,7,1,8,6,1,5,5,6,4,9,2,9,0,6,7,1,5,1,4,1,4,1,2,
%T A155976 8,1,4,4,9,3,7,8,4,6,0,1,9,7,8,2,0,6,4,1,8,0,5,9,8,2,4,1,5,7,5,8,0,2,7,
%U A155976 8,0,2,0,7,1,3,7,2,2,0,7,5,9,1,7,5,9,0,3,2,8,2,4,1,7,7,6,1
%N A155976 Decimal expansion of log_9 (24).
%e A155976 1.4463946303571861556492906715141412814493784601978206418059...
%K A155976 nonn,cons,new
%O A155976 1,2
%A A155976 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155975
%S A155975 1,5,2,8,3,2,0,8,3,3,5,7,3,7,1,8,7,2,7,1,5,1,2,4,6,3,1,4,6,4,9,2,7,2,1,
%T A155975 6,9,5,8,6,6,0,4,8,0,2,5,6,4,1,6,0,3,5,3,4,8,5,2,5,0,8,8,4,8,4,7,0,3,2,
%U A155975 7,4,2,5,9,8,1,1,9,5,2,0,8,4,0,7,6,0,1,5,8,3,0,6,0,2,9,4,1
%N A155975 Decimal expansion of log_8 (24).
%e A155975 1.5283208335737187271512463146492721695866048025641603534852...
%K A155975 nonn,cons,new
%O A155975 1,2
%A A155975 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155964
%S A155964 1,6,3,3,1,9,6,5,9,5,3,7,7,6,4,6,1,4,3,3,4,7,0,8,1,4,0,1,1,7,8,7,8,0,1,
%T A155964 2,4,0,3,6,4,9,9,3,9,9,5,0,5,2,3,3,6,9,5,1,6,4,1,3,8,6,3,5,6,8,0,3,5,5,
%U A155964 0,5,5,2,7,8,1,8,7,5,3,3,0,0,1,9,0,3,7,4,1,2,3,3,6,7,9,8,4
%N A155964 Decimal expansion of log_7 (24).
%e A155964 1.6331965953776461433470814011787801240364993995052336951641...
%K A155964 nonn,cons,new
%O A155964 1,2
%A A155964 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155959
%S A155959 1,7,7,3,7,0,5,6,1,4,4,6,9,0,8,3,1,7,3,7,4,0,4,9,2,2,7,6,9,3,5,6,4,1,7,
%T A155959 5,2,9,3,0,2,8,3,7,1,8,9,1,4,2,0,6,8,5,6,7,7,8,9,8,9,8,5,7,6,5,3,2,8,4,
%U A155959 0,3,7,0,8,1,4,4,5,6,0,7,6,6,3,3,0,4,6,0,0,5,8,9,6,3,2,0,0
%N A155959 Decimal expansion of log_6 (24).
%e A155959 1.7737056144690831737404922769356417529302837189142068567789...
%K A155959 nonn,cons,new
%O A155959 1,2
%A A155959 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155958
%S A155958 1,9,7,4,6,3,5,8,6,8,7,0,6,1,6,4,4,4,7,1,4,4,8,8,6,0,6,5,5,6,2,9,4,9,1,
%T A155958 4,9,2,3,4,0,4,5,1,9,6,1,1,2,4,4,8,5,5,7,6,2,5,9,8,4,8,0,5,3,7,5,7,3,2,
%U A155958 4,1,0,5,4,0,5,6,9,7,9,5,5,8,8,0,4,8,5,1,9,2,5,8,1,2,1,1,6
%N A155958 Decimal expansion of log_5 (24).
%e A155958 1.9746358687061644471448860655629491492340451961124485576259...
%K A155958 nonn,cons,new
%O A155958 1,2
%A A155958 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155936
%S A155936 2,2,9,2,4,8,1,2,5,0,3,6,0,5,7,8,0,9,0,7,2,6,8,6,9,4,7,1,9,7,3,9,0,8,2,
%T A155936 5,4,3,7,9,9,0,7,2,0,3,8,4,6,2,4,0,5,3,0,2,2,7,8,7,6,3,2,7,2,7,0,5,4,9,
%U A155936 1,1,3,8,9,7,1,7,9,2,8,1,2,6,1,1,4,0,2,3,7,4,5,9,0,4,4,1,2
%N A155936 Decimal expansion of log_4 (24).
%e A155936 2.2924812503605780907268694719739082543799072038462405302278...
%K A155936 nonn,cons,new
%O A155936 1,1
%A A155936 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155922
%S A155922 2,8,9,2,7,8,9,2,6,0,7,1,4,3,7,2,3,1,1,2,9,8,5,8,1,3,4,3,0,2,8,2,8,2,5,
%T A155922 6,2,8,9,8,7,5,6,9,2,0,3,9,5,6,4,1,2,8,3,6,1,1,9,6,4,8,3,1,5,1,6,0,5,5,
%U A155922 6,0,4,1,4,2,7,4,4,4,1,5,1,8,3,5,1,8,0,6,5,6,4,8,3,5,5,2,3
%N A155922 Decimal expansion of log_3 (24).
%e A155922 2.8927892607143723112985813430282825628987569203956412836119...
%K A155922 nonn,cons,new
%O A155922 1,1
%A A155922 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155921
%S A155921 4,5,8,4,9,6,2,5,0,0,7,2,1,1,5,6,1,8,1,4,5,3,7,3,8,9,4,3,9,4,7,8,1,6,5,
%T A155921 0,8,7,5,9,8,1,4,4,0,7,6,9,2,4,8,1,0,6,0,4,5,5,7,5,2,6,5,4,5,4,1,0,9,8,
%U A155921 2,2,7,7,9,4,3,5,8,5,6,2,5,2,2,2,8,0,4,7,4,9,1,8,0,8,8,2,4
%N A155921 Decimal expansion of log_2 (24).
%e A155921 4.5849625007211561814537389439478165087598144076924810604557...
%K A155921 nonn,cons,new
%O A155921 1,1
%A A155921 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155920
%S A155920 9,8,6,6,0,8,2,7,7,6,7,8,5,0,1,0,1,5,9,1,2,9,6,9,9,1,1,4,6,9,9,9,2,1,9,
%T A155920 2,2,4,3,1,5,7,9,2,0,8,4,6,1,5,5,4,3,3,2,3,5,4,6,6,3,1,1,8,1,3,2,8,0,7,
%U A155920 5,2,4,2,7,6,6,0,6,3,9,5,7,4,9,2,8,9,0,2,8,7,6,5,8,7,8,2,1
%N A155920 Decimal expansion of log_24 (23).
%e A155920 .98660827767850101591296991146999219224315792084615543323546...
%K A155920 nonn,cons,new
%O A155920 0,1
%A A155920 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155910
%S A155910 1,0,1,4,3,8,0,8,3,2,1,1,1,3,6,0,5,0,9,0,9,3,5,4,9,5,6,5,4,5,9,5,8,2,0,
%T A155910 1,7,8,4,5,5,0,6,0,8,5,4,6,9,3,1,3,1,9,1,8,2,6,2,8,7,9,2,0,4,7,6,3,4,6,
%U A155910 9,6,4,8,1,5,5,0,7,0,7,9,3,2,1,4,1,5,9,1,0,9,6,3,2,3,9,6,8
%N A155910 Decimal expansion of log_22 (23).
%e A155910 1.0143808321113605090935495654595820178455060854693131918262...
%K A155910 nonn,cons,new
%O A155910 1,4
%A A155910 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155909
%S A155909 1,0,2,9,8,8,0,4,7,5,5,3,1,5,7,5,2,8,9,6,0,5,9,9,9,9,8,9,2,6,3,5,6,3,1,
%T A155909 2,6,0,6,5,8,0,6,4,9,0,7,9,8,2,7,7,5,0,3,2,3,4,7,3,4,6,9,6,8,9,6,8,2,5,
%U A155909 9,9,4,7,8,2,4,1,8,2,0,2,6,7,4,3,3,2,2,4,4,2,3,9,8,1,4,6,0
%N A155909 Decimal expansion of log_21 (23).
%e A155909 1.0298804755315752896059999892635631260658064907982775032347...
%K A155909 nonn,cons,new
%O A155909 1,3
%A A155909 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155907
%S A155907 1,0,4,6,6,5,3,6,8,2,5,0,9,9,3,6,6,8,7,3,3,9,7,6,2,7,9,3,0,6,1,5,0,6,7,
%T A155907 5,9,0,0,6,1,7,7,4,8,0,4,8,2,2,1,7,3,4,9,6,8,1,5,9,9,9,1,7,4,7,5,8,1,3,
%U A155907 1,4,5,4,0,7,8,2,1,1,6,5,8,0,1,7,5,7,5,0,8,0,8,1,9,7,2,6,5
%N A155907 Decimal expansion of log_20 (23).
%e A155907 1.0466536825099366873397627930615067590061774804822173496815...
%K A155907 nonn,cons,new
%O A155907 1,3
%A A155907 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155906
%S A155906 1,0,6,4,8,8,6,8,0,4,6,2,2,0,4,5,9,4,4,3,2,1,1,0,1,9,2,0,0,4,0,5,9,1,2,
%T A155906 0,6,3,1,6,0,6,7,1,2,0,4,6,3,0,6,4,0,3,8,5,9,2,1,4,9,6,8,7,0,5,0,8,2,4,
%U A155906 2,1,8,5,4,7,9,9,3,3,9,8,9,9,1,0,6,5,1,9,3,5,9,0,6,1,6,0,3
%N A155906 Decimal expansion of log_19 (23).
%e A155906 1.0648868046220459443211019200405912063160671204630640385921...
%K A155906 nonn,cons,new
%O A155906 1,3
%A A155906 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155889
%S A155889 1,0,8,4,8,0,6,5,5,0,3,5,5,7,9,3,6,8,2,9,4,4,6,5,0,9,3,7,3,2,8,0,9,7,4,
%T A155889 8,9,0,6,4,8,7,3,9,3,2,7,6,7,5,1,2,3,0,2,4,7,9,7,7,8,3,8,7,6,5,2,7,0,4,
%U A155889 2,0,4,5,3,8,0,4,7,0,7,6,2,3,5,1,7,5,5,8,5,7,8,3,2,0,8,3,3
%N A155889 Decimal expansion of log_18 (23).
%e A155889 1.0848065503557936829446509373280974890648739327675123024797...
%K A155889 nonn,cons,new
%O A155889 1,3
%A A155889 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155880
%S A155880 1,1,0,6,6,9,1,8,8,4,8,5,4,7,3,1,1,5,5,3,9,4,5,0,5,4,9,0,5,8,6,0,0,3,2,
%T A155880 1,0,4,0,1,7,3,4,2,2,5,0,8,2,2,6,0,3,1,2,2,0,0,9,6,2,1,4,5,3,4,9,7,8,8,
%U A155880 7,5,5,7,8,6,5,3,4,2,6,0,0,6,1,8,2,5,0,4,1,5,1,8,2,8,0,3,0
%N A155880 Decimal expansion of log_17 (23).
%e A155880 1.1066918848547311553945054905860032104017342250822603122009...
%K A155880 nonn,cons,new
%O A155880 1,4
%A A155880 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155876
%S A155876 1,1,3,0,8,9,0,4,8,9,0,1,4,2,5,3,2,1,8,0,7,3,5,3,7,0,6,1,0,4,0,6,6,7,2,
%T A155876 1,1,1,2,4,7,0,6,2,8,1,3,6,0,6,3,8,7,6,4,8,7,3,6,1,0,9,3,3,0,0,3,6,9,4,
%U A155876 5,3,6,3,9,0,6,9,1,1,7,4,0,2,7,6,8,8,6,3,1,4,6,5,5,2,2,0,5
%N A155876 Decimal expansion of log_16 (23).
%e A155876 1.1308904890142532180735370610406672111247062813606387648736...
%K A155876 nonn,cons,new
%O A155876 1,3
%A A155876 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155855
%S A155855 1,1,5,7,8,4,1,9,8,3,3,7,7,1,7,8,3,8,5,3,5,4,7,6,4,9,2,1,7,2,0,4,3,3,9,
%T A155855 0,0,0,5,1,9,9,6,2,0,2,6,3,8,2,4,8,1,2,7,8,1,9,8,3,3,6,9,2,4,3,6,0,8,5,
%U A155855 8,6,3,2,8,7,7,3,4,6,3,5,9,7,6,4,9,4,8,8,4,4,3,8,2,0,5,5,2
%N A155855 Decimal expansion of log_15 (23).
%e A155855 1.1578419833771783853547649217204339000519962026382481278198...
%K A155855 nonn,cons,new
%O A155855 1,3
%A A155855 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155840
%S A155840 1,1,8,8,1,1,1,4,4,4,4,7,0,3,1,2,1,8,3,0,4,5,2,3,6,7,3,1,6,5,9,5,7,0,5,
%T A155840 8,6,9,7,4,4,1,9,1,9,2,1,8,4,0,8,8,1,4,6,7,8,5,1,6,3,4,5,8,9,3,2,4,0,0,
%U A155840 6,0,1,9,8,6,8,4,6,7,1,5,1,0,7,0,1,3,7,4,2,2,8,7,0,5,7,3,0
%N A155840 Decimal expansion of log_14 (23).
%e A155840 1.1881114444703121830452367316595705869744191921840881467851...
%K A155840 nonn,cons,new
%O A155840 1,3
%A A155840 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155837
%S A155837 1,2,2,2,4,3,9,0,3,4,4,4,2,4,8,3,6,0,2,1,5,3,1,6,0,2,6,3,7,0,8,4,7,2,5,
%T A155837 5,6,5,0,9,5,4,9,1,6,1,3,9,2,0,8,7,7,6,5,0,1,1,0,3,9,4,2,6,0,3,0,0,1,9,
%U A155837 1,9,9,7,8,2,6,0,3,9,8,5,9,5,1,3,4,5,7,8,9,2,8,1,1,6,1,1,6
%N A155837 Decimal expansion of log_13 (23).
%e A155837 1.2224390344424836021531602637084725565095491613920877650110...
%K A155837 nonn,cons,new
%O A155837 1,2
%A A155837 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155832
%S A155832 1,2,6,1,8,1,5,6,9,6,8,5,7,9,2,9,9,4,5,6,1,3,0,1,4,0,4,4,9,9,2,0,3,3,9,
%T A155832 8,3,2,6,4,3,4,2,5,8,7,5,0,1,4,9,9,3,1,3,9,8,6,4,2,7,6,8,2,9,3,4,3,9,2,
%U A155832 7,3,7,0,6,1,9,3,1,5,4,6,3,8,7,2,5,0,4,2,8,0,6,3,7,3,2,9,4
%N A155832 Decimal expansion of log_12 (23).
%e A155832 1.2618156968579299456130140449920339832643425875014993139864...
%K A155832 nonn,cons,new
%O A155832 1,2
%A A155832 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155831
%S A155831 1,3,0,7,6,0,2,6,5,1,1,6,5,8,2,5,4,9,8,4,7,8,5,0,6,0,7,3,6,4,2,6,2,7,3,
%T A155831 6,2,1,7,7,2,9,3,7,7,3,6,1,2,0,7,4,7,3,1,3,9,9,1,7,6,4,6,7,8,5,1,2,1,6,
%U A155831 2,5,7,0,3,7,0,3,4,5,4,5,0,7,7,2,3,6,8,1,3,0,6,3,7,5,1,7,8
%N A155831 Decimal expansion of log_11 (23).
%e A155831 1.3076026511658254984785060736426273621772937736120747313991...
%K A155831 nonn,cons,new
%O A155831 1,2
%A A155831 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155830
%S A155830 1,3,6,1,7,2,7,8,3,6,0,1,7,5,9,2,8,7,8,8,6,7,7,7,7,1,1,2,2,5,1,1,8,9,5,
%T A155830 4,9,6,9,7,5,1,1,0,3,4,3,3,6,0,9,6,1,8,8,2,7,5,6,0,5,4,8,6,6,1,4,6,8,8,
%U A155830 6,3,6,3,9,6,8,0,6,4,7,2,6,7,3,5,8,4,1,9,0,8,2,7,2,1,4,8,0
%N A155830 Decimal expansion of log_10 (23).
%e A155830 1.3617278360175928788677771122511895496975110343360961882756...
%K A155830 nonn,cons,new
%O A155830 1,2
%A A155830 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155829
%S A155829 1,4,2,7,0,2,4,9,1,5,1,0,0,1,3,5,5,5,3,7,0,1,8,1,5,8,8,2,4,7,4,6,0,3,9,
%T A155829 4,1,3,8,1,5,9,0,8,1,8,5,2,5,2,4,4,8,8,3,5,8,6,7,5,5,8,8,3,8,2,7,3,9,2,
%U A155829 5,7,2,7,4,9,7,4,1,7,0,0,7,6,6,2,1,6,4,5,7,7,1,6,0,9,0,1,9
%N A155829 Decimal expansion of log_9 (23).
%e A155829 1.4270249151001355537018158824746039413815908185252448835867...
%K A155829 nonn,cons,new
%O A155829 1,2
%A A155829 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155827
%S A155827 1,5,0,7,8,5,3,9,8,5,3,5,2,3,3,7,6,2,4,0,9,8,0,4,9,4,1,4,7,2,0,8,8,9,6,
%T A155827 1,4,8,3,2,9,4,1,7,0,8,4,8,0,8,5,1,6,8,6,4,9,8,1,4,7,9,1,0,6,7,1,5,9,2,
%U A155827 7,1,5,1,8,7,5,8,8,2,3,2,0,3,6,9,1,8,1,7,5,2,8,7,3,6,2,7,3
%N A155827 Decimal expansion of log_8 (23).
%e A155827 1.5078539853523376240980494147208896148329417084808516864981...
%K A155827 nonn,cons,new
%O A155827 1,2
%A A155827 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155824
%S A155824 1,6,1,1,3,2,5,2,8,0,0,7,5,9,3,1,1,7,4,9,5,2,6,9,5,5,6,1,8,6,2,5,9,4,5,
%T A155824 1,4,2,3,1,6,0,1,2,8,4,3,9,9,0,1,9,4,2,0,9,8,4,8,0,2,5,8,4,7,2,4,1,1,6,
%U A155824 1,7,1,8,2,1,5,1,6,4,9,3,1,2,0,8,6,1,3,3,3,4,0,9,0,3,1,8,3
%N A155824 Decimal expansion of log_7 (23).
%e A155824 1.6113252800759311749526955618625945142316012843990194209848...
%K A155824 nonn,cons,new
%O A155824 1,2
%A A155824 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155823
%S A155823 1,7,4,9,9,5,2,6,4,1,4,0,0,0,2,9,4,8,1,1,6,1,6,1,0,2,0,7,7,9,7,2,9,2,6,
%T A155823 7,3,7,6,8,0,7,7,5,9,7,7,1,2,8,6,0,4,8,5,0,8,3,2,7,0,2,0,9,0,5,9,2,4,3,
%U A155823 9,6,5,1,3,7,2,3,5,4,1,8,7,0,9,9,5,5,3,0,4,8,4,7,0,1,4,3,9
%N A155823 Decimal expansion of log_6 (23).
%e A155823 1.7499526414000294811616102077972926737680775977128604850832...
%K A155823 nonn,cons,new
%O A155823 1,2
%A A155823 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155821
%S A155821 1,9,4,8,1,9,2,0,9,3,4,6,6,3,7,9,5,6,7,4,5,1,5,9,6,0,5,8,8,8,9,2,2,7,4,
%T A155821 2,3,9,8,4,6,4,8,3,6,4,8,9,6,3,8,8,0,0,8,1,3,9,6,5,3,0,1,2,3,0,3,0,6,3,
%U A155821 3,5,7,5,3,0,4,9,4,5,7,7,4,0,2,0,0,2,5,1,1,3,3,5,3,3,8,8,6
%N A155821 Decimal expansion of log_5 (23).
%e A155821 1.9481920934663795674515960588892274239846483648963880081396...
%K A155821 nonn,cons,new
%O A155821 1,2
%A A155821 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155818
%S A155818 2,2,6,1,7,8,0,9,7,8,0,2,8,5,0,6,4,3,6,1,4,7,0,7,4,1,2,2,0,8,1,3,3,4,4,
%T A155818 2,2,2,4,9,4,1,2,5,6,2,7,2,1,2,7,7,5,2,9,7,4,7,2,2,1,8,6,6,0,0,7,3,8,9,
%U A155818 0,7,2,7,8,1,3,8,2,3,4,8,0,5,5,3,7,7,2,6,2,9,3,1,0,4,4,1,0
%N A155818 Decimal expansion of log_4 (23).
%e A155818 2.2617809780285064361470741220813344222494125627212775297472...
%K A155818 nonn,cons,new
%O A155818 1,1
%A A155818 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155808
%S A155808 2,8,5,4,0,4,9,8,3,0,2,0,0,2,7,1,1,0,7,4,0,3,6,3,1,7,6,4,9,4,9,2,0,7,8,
%T A155808 8,2,7,6,3,1,8,1,6,3,7,0,5,0,4,8,9,7,6,7,1,7,3,5,1,1,7,6,7,6,5,4,7,8,5,
%U A155808 1,4,5,4,9,9,4,8,3,4,0,1,5,3,2,4,3,2,9,1,5,4,3,2,1,8,0,3,8
%N A155808 Decimal expansion of log_3 (23).
%e A155808 2.8540498302002711074036317649492078827631816370504897671735...
%K A155808 nonn,cons,new
%O A155808 1,1
%A A155808 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155793
%S A155793 4,5,2,3,5,6,1,9,5,6,0,5,7,0,1,2,8,7,2,2,9,4,1,4,8,2,4,4,1,6,2,6,6,8,8,
%T A155793 4,4,4,9,8,8,2,5,1,2,5,4,4,2,5,5,5,0,5,9,4,9,4,4,4,3,7,3,2,0,1,4,7,7,8,
%U A155793 1,4,5,5,6,2,7,6,4,6,9,6,1,1,0,7,5,4,5,2,5,8,6,2,0,8,8,2,1
%N A155793 Decimal expansion of log_2 (23).
%e A155793 4.5235619560570128722941482441626688444988251254425550594944...
%K A155793 nonn,cons,new
%O A155793 1,1
%A A155793 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155792
%S A155792 9,7,2,6,2,1,1,7,5,8,4,0,7,8,0,7,0,0,6,1,1,8,3,2,7,1,7,8,0,8,8,7,6,2,8,
%T A155792 5,0,0,6,8,3,3,7,2,5,4,9,6,1,2,5,1,0,3,2,1,7,5,5,4,9,1,2,2,9,0,8,8,1,2,
%U A155792 7,3,5,4,3,7,0,5,8,9,1,5,4,1,8,4,2,7,7,4,7,4,7,5,8,7,3,8,2
%N A155792 Decimal expansion of log_24 (22).
%e A155792 .97262117584078070061183271780887628500683372549612510321755...
%K A155792 nonn,cons,new
%O A155792 0,1
%A A155792 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155791
%S A155791 9,8,5,8,2,3,0,4,4,3,0,8,2,9,2,1,3,8,4,5,9,5,6,7,9,3,1,9,0,4,0,6,1,2,9,
%T A155791 4,2,0,5,7,9,3,3,0,4,0,8,2,6,9,4,5,2,5,4,0,6,6,3,0,8,8,7,5,2,4,5,4,1,6,
%U A155791 5,0,4,7,3,9,0,0,8,5,5,7,7,4,1,8,1,9,9,4,3,4,0,3,9,5,5,9,6
%N A155791 Decimal expansion of log_23 (22).
%e A155791 .98582304430829213845956793190406129420579330408269452540663...
%K A155791 nonn,cons,new
%O A155791 0,1
%A A155791 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155790
%S A155790 1,0,1,5,2,7,9,9,0,5,6,6,2,2,0,9,1,2,4,2,7,3,9,5,4,5,4,2,8,6,8,7,9,3,2,
%T A155790 9,0,1,4,3,6,9,9,0,4,1,0,0,7,9,0,9,4,6,2,2,5,2,0,3,6,6,9,8,1,4,0,8,7,7,
%U A155790 9,5,7,1,6,7,7,1,3,0,8,2,1,6,7,6,1,4,9,6,1,0,2,8,2,2,4,2,4
%N A155790 Decimal expansion of log_21 (22).
%e A155790 1.0152799056622091242739545428687932901436990410079094622520...
%K A155790 nonn,cons,new
%O A155790 1,4
%A A155790 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155789
%S A155789 1,0,3,1,8,1,5,3,1,9,6,2,8,4,3,0,4,4,7,3,6,8,1,3,1,2,7,4,7,6,9,3,1,1,2,
%T A155789 4,9,4,1,2,7,4,9,3,1,2,6,5,5,2,5,1,9,0,4,7,8,3,9,9,4,4,3,5,9,6,0,9,4,1,
%U A155789 7,8,6,4,0,8,5,4,9,8,6,4,4,1,5,8,5,2,7,9,8,3,9,4,0,3,7,8,6
%N A155789 Decimal expansion of log_20 (22).
%e A155789 1.0318153196284304473681312747693112494127493126552519047839...
%K A155789 nonn,cons,new
%O A155789 1,3
%A A155789 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155787
%S A155787 1,0,4,9,7,8,9,9,5,1,5,7,6,2,3,4,8,3,2,5,5,2,7,8,9,8,6,0,8,6,9,7,1,9,5,
%T A155787 3,0,4,0,3,2,2,4,8,4,4,9,6,3,1,9,4,8,2,1,4,9,3,8,0,1,9,2,0,0,1,2,3,8,4,
%U A155787 7,4,0,3,0,1,6,6,6,0,1,6,2,5,6,2,2,1,5,7,3,8,6,9,8,0,3,5,7
%N A155787 Decimal expansion of log_19 (22).
%e A155787 1.0497899515762348325527898608697195304032248449631948214938...
%K A155787 nonn,cons,new
%O A155787 1,3
%A A155787 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155784
%S A155784 1,0,6,9,4,2,7,2,9,5,9,5,7,3,2,5,1,4,2,7,8,0,6,0,1,2,6,8,6,1,9,1,2,9,8,
%T A155784 9,7,1,4,2,5,9,8,0,5,6,7,2,6,6,8,1,9,3,6,1,6,1,6,0,5,4,1,5,3,0,6,1,0,1,
%U A155784 3,5,9,2,3,2,5,0,8,3,6,8,1,0,6,0,7,3,0,6,4,3,0,0,7,0,9,1,5
%N A155784 Decimal expansion of log_18 (22).
%e A155784 1.0694272959573251427806012686191298971425980567266819361616...
%K A155784 nonn,cons,new
%O A155784 1,3
%A A155784 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155783
%S A155783 1,0,9,1,0,0,2,3,6,3,0,3,8,7,7,2,9,7,3,2,1,0,3,6,3,4,1,1,6,9,3,6,8,5,6,
%T A155783 9,0,1,7,2,2,1,7,3,0,6,2,8,9,7,7,0,7,2,6,4,9,5,5,0,0,1,5,5,3,0,1,9,4,1,
%U A155783 5,8,0,9,7,6,4,2,9,7,8,0,5,4,8,7,9,7,0,3,8,6,4,9,1,4,9,2,0
%N A155783 Decimal expansion of log_17 (22).
%e A155783 1.0910023630387729732103634116936856901722173062897707264955...
%K A155783 nonn,cons,new
%O A155783 1,3
%A A155783 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155782
%S A155782 1,1,1,4,8,5,7,9,0,4,6,5,9,3,2,4,3,1,4,0,4,9,8,4,0,7,6,1,6,8,1,4,4,8,2,
%T A155782 3,9,6,7,5,8,0,7,8,8,1,4,2,0,4,4,2,0,1,7,8,2,8,2,0,0,4,1,1,4,3,1,5,8,2,
%U A155782 6,5,4,9,3,0,0,0,4,5,8,8,1,7,7,3,7,2,8,2,4,8,2,1,7,2,5,1,2
%N A155782 Decimal expansion of log_16 (22).
%e A155782 1.1148579046593243140498407616814482396758078814204420178282...
%K A155782 nonn,cons,new
%O A155782 1,4
%A A155782 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155781
%S A155781 1,1,4,1,4,2,7,3,0,8,8,8,0,8,4,0,9,7,7,0,3,5,0,5,7,2,0,5,6,3,5,6,1,4,6,
%T A155781 1,5,7,0,7,8,3,0,3,8,4,6,5,9,9,3,2,8,2,4,1,7,0,2,0,7,4,1,6,4,5,5,1,3,2,
%U A155781 8,8,2,4,8,0,5,5,8,5,0,6,6,3,6,7,3,6,8,6,6,9,1,5,5,3,1,2,5
%N A155781 Decimal expansion of log_15 (22).
%e A155781 1.1414273088808409770350572056356146157078303846599328241702...
%K A155781 nonn,cons,new
%O A155781 1,3
%A A155781 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155773
%S A155773 1,1,7,1,2,6,7,6,4,1,1,6,5,2,4,5,5,4,1,8,6,3,9,7,9,2,0,4,3,5,0,4,8,0,7,
%T A155773 6,1,5,3,8,1,8,7,6,6,3,3,2,9,0,3,8,4,4,6,5,5,0,4,9,6,8,1,2,0,9,0,3,8,1,
%U A155773 3,0,7,1,7,5,7,1,8,6,1,6,7,7,1,5,7,1,1,0,6,1,8,1,3,3,6,5,2
%N A155773 Decimal expansion of log_14 (22).
%e A155773 1.1712676411652455418639792043504807615381876633290384465504...
%K A155773 nonn,cons,new
%O A155773 1,3
%A A155773 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155759
%S A155759 1,2,0,5,1,0,8,5,7,0,4,1,5,3,7,8,3,7,1,6,5,9,4,3,6,0,9,2,0,6,4,1,9,8,0,
%T A155759 6,8,5,1,2,7,4,1,6,5,1,8,8,9,7,1,1,8,5,4,8,0,7,7,3,2,0,5,7,5,0,7,4,9,2,
%U A155759 5,6,5,1,1,2,8,5,2,0,1,5,5,5,6,3,5,8,6,2,1,2,5,9,9,5,1,9,6
%N A155759 Decimal expansion of log_13 (22).
%e A155759 1.2051085704153783716594360920641980685127416518897118548077...
%K A155759 nonn,cons,new
%O A155759 1,2
%A A155759 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155749
%S A155749 1,2,4,3,9,2,6,9,9,1,6,3,2,4,7,3,5,9,4,0,4,9,1,5,7,0,8,7,2,8,5,1,4,0,5,
%T A155749 1,5,6,8,6,6,0,2,1,0,9,4,6,1,7,6,6,9,4,5,9,8,0,0,0,2,4,3,8,1,6,4,6,4,2,
%U A155749 8,0,8,8,9,6,1,0,0,8,8,6,4,7,4,4,0,9,6,7,4,1,2,5,0,5,6,9,8
%N A155749 Decimal expansion of log_12 (22).
%e A155749 1.2439269916324735940491570872851405156866021094617669459800...
%K A155749 nonn,cons,new
%O A155749 1,2
%A A155749 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155748
%S A155748 1,2,8,9,0,6,4,8,2,6,3,1,7,8,8,7,8,5,9,2,6,6,2,1,1,0,0,7,7,0,0,2,6,3,5,
%T A155748 6,6,1,9,1,2,9,4,6,1,5,9,8,5,6,9,6,0,0,3,6,2,6,3,4,1,5,6,7,7,9,8,5,3,1,
%U A155748 5,8,3,5,5,6,9,1,5,7,7,1,9,3,2,9,7,7,0,9,1,5,3,9,1,9,7,8,1
%N A155748 Decimal expansion of log_11 (22).
%e A155748 1.2890648263178878592662110077002635661912946159856960036263...
%K A155748 nonn,cons,new
%O A155748 1,2
%A A155748 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155746
%S A155746 1,3,4,2,4,2,2,6,8,0,8,2,2,2,0,6,2,3,5,9,6,3,9,3,8,8,6,5,9,6,7,5,1,7,2,
%T A155746 6,8,4,7,4,8,9,2,0,7,1,9,2,8,5,6,1,6,3,5,9,0,6,9,6,6,4,7,9,8,0,6,8,6,1,
%U A155746 2,2,1,5,0,7,6,7,3,8,5,7,0,5,8,2,2,2,0,3,8,5,0,3,9,1,7,3,5
%N A155746 Decimal expansion of log_10 (22).
%e A155746 1.3424226808222062359639388659675172684748920719285616359069...
%K A155746 nonn,cons,new
%O A155746 1,2
%A A155746 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155743
%S A155743 1,4,0,6,7,9,4,0,4,6,1,0,7,7,9,7,7,5,9,0,7,4,2,5,3,7,6,4,5,3,7,3,4,4,8,
%T A155743 8,8,9,2,1,2,7,3,5,8,2,6,6,6,4,1,2,3,9,4,0,5,3,9,7,3,9,7,7,0,0,5,2,4,6,
%U A155743 9,1,7,6,3,6,1,6,3,5,8,4,1,9,3,2,1,6,8,5,9,3,5,6,7,1,1,3,2
%N A155743 Decimal expansion of log_9 (22).
%e A155743 1.4067940461077977590742537645373448889212735826664123940539...
%K A155743 nonn,cons,new
%O A155743 1,2
%A A155743 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155741
%S A155741 1,4,8,6,4,7,7,2,0,6,2,1,2,4,3,2,4,1,8,7,3,3,1,2,1,0,1,5,5,7,5,2,6,4,3,
%T A155741 1,9,5,6,7,7,4,3,8,4,1,8,9,3,9,2,2,6,9,0,4,3,7,6,0,0,5,4,8,5,7,5,4,4,3,
%U A155741 5,3,9,9,0,6,6,7,2,7,8,4,2,3,6,4,9,7,0,9,9,7,6,2,3,0,0,1,6
%N A155741 Decimal expansion of log_8 (22).
%e A155741 1.4864772062124324187331210155752643195677438418939226904376...
%K A155741 nonn,cons,new
%O A155741 1,2
%A A155741 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155735
%S A155735 1,5,8,8,4,8,1,5,9,2,9,7,5,3,6,5,9,3,8,3,7,4,9,3,3,9,4,5,6,5,6,9,1,9,8,
%T A155735 2,8,4,5,0,5,9,7,0,5,6,0,5,9,6,3,1,2,5,5,6,6,5,8,9,9,5,9,2,5,8,7,6,9,7,
%U A155735 0,8,4,6,0,1,0,2,9,4,3,5,5,5,2,5,4,7,8,2,5,8,4,6,8,9,3,9,7
%N A155735 Decimal expansion of log_7 (22).
%e A155735 1.5884815929753659383749339456569198284505970560596312556658...
%K A155735 nonn,cons,new
%O A155735 1,2
%A A155735 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155697
%S A155697 1,7,2,5,1,4,3,6,4,0,3,4,0,3,1,4,1,2,6,8,2,8,6,6,3,7,4,9,3,4,0,8,0,4,0,
%T A155697 7,4,8,7,6,7,9,8,6,7,6,6,7,8,1,4,3,2,8,4,9,6,1,0,9,9,4,9,1,0,3,4,9,7,3,
%U A155697 6,3,9,4,1,5,5,7,9,9,4,2,2,4,0,8,9,1,7,3,5,6,8,5,8,5,1,2,2
%N A155697 Decimal expansion of log_6 (22).
%e A155697 1.7251436403403141268286637493408040748767986766781432849610...
%K A155697 nonn,cons,new
%O A155697 1,2
%A A155697 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155696
%S A155696 1,9,2,0,5,7,2,6,6,0,4,7,8,3,7,1,1,2,3,4,6,9,3,0,8,3,4,8,7,4,7,9,3,6,9,
%T A155696 3,9,6,8,3,2,7,2,3,7,6,6,3,9,3,9,4,1,9,9,8,4,9,3,2,8,6,4,4,4,7,1,9,6,0,
%U A155696 9,0,5,0,7,3,2,9,2,4,2,0,9,1,8,3,2,3,0,2,2,8,3,9,6,8,6,5,3
%N A155696 Decimal expansion of log_5 (22).
%e A155696 1.9205726604783711234693083487479369396832723766393941998493...
%K A155696 nonn,cons,new
%O A155696 1,2
%A A155696 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155695
%S A155695 2,2,2,9,7,1,5,8,0,9,3,1,8,6,4,8,6,2,8,0,9,9,6,8,1,5,2,3,3,6,2,8,9,6,4,
%T A155695 7,9,3,5,1,6,1,5,7,6,2,8,4,0,8,8,4,0,3,5,6,5,6,4,0,0,8,2,2,8,6,3,1,6,5,
%U A155695 3,0,9,8,6,0,0,0,9,1,7,6,3,5,4,7,4,5,6,4,9,6,4,3,4,5,0,2,4
%N A155695 Decimal expansion of log_4 (22).
%e A155695 2.2297158093186486280996815233628964793516157628408840356564...
%K A155695 nonn,cons,new
%O A155695 1,1
%A A155695 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155694
%S A155694 2,8,1,3,5,8,8,0,9,2,2,1,5,5,9,5,5,1,8,1,4,8,5,0,7,5,2,9,0,7,4,6,8,9,7,
%T A155694 7,7,8,4,2,5,4,7,1,6,5,3,3,2,8,2,4,7,8,8,1,0,7,9,4,7,9,5,4,0,1,0,4,9,3,
%U A155694 8,3,5,2,7,2,3,2,7,1,6,8,3,8,6,4,3,3,7,1,8,7,1,3,4,2,2,6,4
%N A155694 Decimal expansion of log_3 (22).
%e A155694 2.8135880922155955181485075290746897778425471653328247881079...
%K A155694 nonn,cons,new
%O A155694 1,1
%A A155694 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155693
%S A155693 4,4,5,9,4,3,1,6,1,8,6,3,7,2,9,7,2,5,6,1,9,9,3,6,3,0,4,6,7,2,5,7,9,2,9,
%T A155693 5,8,7,0,3,2,3,1,5,2,5,6,8,1,7,6,8,0,7,1,3,1,2,8,0,1,6,4,5,7,2,6,3,3,0,
%U A155693 6,1,9,7,2,0,0,1,8,3,5,2,7,0,9,4,9,1,2,9,9,2,8,6,9,0,0,4,8
%N A155693 Decimal expansion of log_2 (22).
%e A155693 4.4594316186372972561993630467257929587032315256817680713128...
%K A155693 nonn,cons,new
%O A155693 1,1
%A A155693 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155692
%S A155692 9,5,7,9,8,3,2,8,1,6,7,0,8,7,6,2,0,0,9,6,9,8,9,1,8,0,5,7,9,3,2,6,5,4,0,
%T A155692 5,3,2,3,6,6,0,1,1,9,3,1,5,1,2,0,1,1,4,7,0,3,2,8,3,9,2,1,2,1,8,2,1,6,5,
%U A155692 0,7,4,7,9,3,1,8,2,7,9,8,5,8,2,1,1,9,0,8,0,8,5,4,8,8,2,4,6
%N A155692 Decimal expansion of log_24 (21).
%e A155692 .95798328167087620096989180579326540532366011931512011470328...
%K A155692 nonn,cons,new
%O A155692 0,1
%A A155692 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155691
%S A155691 9,7,0,9,8,6,4,6,2,7,5,8,0,6,6,7,4,5,4,2,0,9,9,1,8,3,5,6,9,3,4,5,0,9,8,
%T A155691 3,6,1,6,4,5,3,7,0,5,7,6,7,0,5,4,8,7,8,5,3,3,5,3,7,7,0,8,5,2,5,8,5,4,1,
%U A155691 1,7,8,7,8,1,2,6,2,9,5,0,7,1,7,1,6,2,5,6,1,7,4,6,5,9,1,5,1
%N A155691 Decimal expansion of log_23 (21).
%e A155691 .97098646275806674542099183569345098361645370576705487853353...
%K A155691 nonn,cons,new
%O A155691 0,1
%A A155691 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155690
%S A155690 9,8,4,9,5,0,0,5,6,0,6,1,3,9,4,3,0,6,7,4,7,3,6,1,1,0,6,8,4,0,1,3,8,9,3,
%T A155690 7,9,4,9,8,6,5,9,3,7,5,9,6,6,9,4,0,9,8,3,2,7,0,3,4,3,8,9,3,6,2,1,7,7,2,
%U A155690 5,6,8,9,5,4,7,9,9,4,0,3,0,9,6,1,1,5,1,4,4,7,0,4,5,0,9,3,5
%N A155690 Decimal expansion of log_22 (21).
%e A155690 .98495005606139430674736110684013893794986593759669409832703...
%K A155690 nonn,cons,new
%O A155690 0,1
%A A155690 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155687
%S A155687 1,0,1,6,2,8,6,5,5,6,9,1,3,0,2,8,0,5,4,5,6,7,2,4,0,2,5,6,2,1,6,9,3,5,9,
%T A155687 6,3,3,0,4,0,2,6,9,7,2,5,7,0,0,1,0,8,2,1,5,0,8,4,1,2,7,3,6,8,4,8,3,9,0,
%U A155687 7,4,0,8,7,1,0,9,8,8,7,6,4,5,1,2,1,0,6,3,8,5,2,9,4,6,3,0,2
%N A155687 Decimal expansion of log_20 (21).
%e A155687 1.0162865569130280545672402562169359633040269725700108215084...
%K A155687 nonn,cons,new
%O A155687 1,4
%A A155687 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155686
%S A155686 1,0,3,3,9,9,0,6,7,1,6,5,7,7,0,0,9,1,2,8,9,9,3,8,9,7,2,0,2,1,7,1,3,7,9,
%T A155686 2,4,8,0,6,9,5,9,9,5,7,7,3,2,8,4,3,9,2,1,8,7,8,4,7,8,3,3,4,8,1,4,6,5,5,
%U A155686 3,8,6,9,9,0,3,4,8,2,8,6,6,0,4,9,7,0,2,3,2,6,5,3,5,7,1,8,0
%N A155686 Decimal expansion of log_19 (21).
%e A155686 1.0339906716577009128993897202171379248069599577328439218784...
%K A155686 nonn,cons,new
%O A155686 1,3
%A A155686 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155685
%S A155685 1,0,5,3,3,3,2,4,7,5,1,0,6,7,5,2,7,2,0,4,4,3,9,6,6,1,6,5,5,8,9,1,7,2,3,
%T A155685 2,0,1,6,1,7,6,9,4,3,7,7,6,2,6,2,3,2,4,2,0,1,9,4,5,9,8,0,5,7,5,3,1,7,0,
%U A155685 1,2,3,9,4,5,8,5,5,4,3,0,6,8,9,2,5,9,4,7,5,0,2,0,4,6,8,7,0
%N A155685 Decimal expansion of log_18 (21).
%e A155685 1.0533324751067527204439661655891723201617694377626232420194...
%K A155685 nonn,cons,new
%O A155685 1,3
%A A155685 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155684
%S A155684 1,0,7,4,5,8,2,8,3,8,6,3,8,1,5,3,1,0,3,8,7,3,3,3,2,1,9,3,5,1,5,7,1,8,0,
%T A155684 8,5,7,7,5,8,4,4,5,7,1,0,1,5,1,7,6,5,2,4,8,1,2,0,8,3,8,0,2,2,4,3,9,7,7,
%U A155684 9,2,3,5,1,5,6,3,5,0,9,6,0,5,5,9,3,8,2,7,6,9,1,2,5,0,8,8,9
%N A155684 Decimal expansion of log_17 (21).
%e A155684 1.0745828386381531038733321935157180857758445710151765248120...
%K A155684 nonn,cons,new
%O A155684 1,3
%A A155684 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155683
%S A155683 1,0,9,8,0,7,9,3,5,5,6,9,4,6,9,0,0,7,2,2,2,3,9,2,7,0,6,5,2,9,4,9,1,1,8,
%T A155683 2,9,3,5,0,2,1,0,2,5,8,4,1,4,6,5,5,4,6,1,0,3,3,2,6,1,0,9,4,6,5,2,8,5,4,
%U A155683 7,6,9,1,6,4,1,3,7,8,8,7,2,5,5,0,3,5,3,6,8,5,2,2,0,7,4,7,5
%N A155683 Decimal expansion of log_16 (21).
%e A155683 1.0980793556946900722239270652949118293502102584146554610332...
%K A155683 nonn,cons,new
%O A155683 1,3
%A A155683 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155682
%S A155682 1,1,2,4,2,4,8,8,9,1,8,7,2,1,9,0,7,5,5,9,8,9,0,1,9,5,5,4,0,7,8,1,7,7,8,
%T A155682 6,7,9,8,3,3,0,8,1,3,8,2,6,2,0,8,9,4,4,0,8,9,4,5,6,5,2,0,5,5,5,2,1,4,7,
%U A155682 3,6,1,2,2,0,2,6,2,6,4,5,5,2,3,7,4,1,0,7,4,4,4,3,0,2,5,2,7
%N A155682 Decimal expansion of log_15 (21).
%e A155682 1.1242488918721907559890195540781778679833081382620894408945...
%K A155682 nonn,cons,new
%O A155682 1,3
%A A155682 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155681
%S A155681 1,1,5,3,6,4,0,1,2,8,8,2,8,6,0,5,6,6,6,5,5,7,6,3,3,8,2,3,7,7,7,4,7,1,0,
%T A155681 0,8,3,8,6,1,3,7,3,9,9,0,1,7,4,9,6,1,0,6,8,5,4,3,6,3,6,7,1,5,5,6,4,0,3,
%U A155681 6,9,5,1,7,9,5,9,2,3,3,7,6,1,0,7,2,2,7,2,9,9,8,3,5,3,6,9,9
%N A155681 Decimal expansion of log_14 (21).
%e A155681 1.1536401288286056665576338237774710083861373990174961068543...
%K A155681 nonn,cons,new
%O A155681 1,3
%A A155681 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155680
%S A155680 1,1,8,6,9,7,1,7,5,3,9,9,0,6,9,3,6,7,5,6,6,3,1,0,5,9,5,3,7,1,0,6,6,8,8,
%T A155680 8,4,1,1,5,2,8,2,7,0,3,4,6,8,7,6,5,9,0,7,0,0,0,8,0,8,0,2,0,9,5,4,3,3,6,
%U A155680 8,8,2,6,5,4,8,4,7,2,7,9,8,6,2,1,2,4,5,8,9,7,3,5,5,9,2,1,9
%N A155680 Decimal expansion of log_13 (21).
%e A155680 1.1869717539906936756631059537106688841152827034687659070008...
%K A155680 nonn,cons,new
%O A155680 1,3
%A A155680 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155679
%S A155679 1,2,2,5,2,0,5,9,6,0,1,4,4,6,8,6,4,3,3,1,7,2,8,4,4,7,1,6,5,3,9,0,3,9,4,
%T A155679 8,0,5,5,3,8,9,1,4,4,9,5,5,2,1,5,0,6,3,2,2,3,3,2,5,6,5,6,5,7,9,0,3,6,3,
%U A155679 0,6,0,2,2,2,0,8,9,1,6,4,3,7,9,4,9,4,9,6,0,8,7,8,5,1,8,4,8
%N A155679 Decimal expansion of log_12 (21).
%e A155679 1.2252059601446864331728447165390394805538914495521506322332...
%K A155679 nonn,cons,new
%O A155679 1,2
%A A155679 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155678
%S A155678 1,2,6,9,6,6,4,4,7,2,9,4,8,5,7,5,1,6,2,1,5,0,1,6,8,8,2,6,8,3,3,2,9,3,8,
%T A155678 5,7,0,1,8,6,0,0,1,8,3,5,7,7,7,3,3,1,6,7,0,3,5,6,1,8,9,7,8,2,8,4,6,6,1,
%U A155678 9,7,1,7,4,0,6,4,3,7,6,7,8,8,6,2,2,2,7,3,9,7,9,1,7,7,3,3,0
%N A155678 Decimal expansion of log_11 (21).
%e A155678 1.2696644729485751621501688268332938570186001835777331670356...
%K A155678 nonn,cons,new
%O A155678 1,2
%A A155678 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155677
%S A155677 1,3,2,2,2,1,9,2,9,4,7,3,3,9,1,9,2,6,8,0,0,7,2,4,4,1,6,1,8,4,7,7,5,1,5,
%T A155677 0,2,6,8,3,7,0,1,2,6,0,5,1,4,6,6,1,2,7,1,3,3,3,5,0,0,5,9,4,0,2,3,4,8,2,
%U A155677 5,9,2,6,8,5,7,4,0,2,8,9,1,0,9,0,7,9,8,8,3,4,9,5,1,0,4,8,7
%N A155677 Decimal expansion of log_10 (21).
%e A155677 1.3222192947339192680072441618477515026837012605146612713335...
%K A155677 nonn,cons,new
%O A155677 1,2
%A A155677 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155676
%S A155676 1,3,8,5,6,2,1,8,7,4,5,8,0,7,1,1,1,3,0,0,3,3,9,6,4,1,5,3,5,4,1,2,2,8,8,
%T A155676 5,9,0,3,3,2,3,5,6,6,7,2,9,7,1,2,1,7,3,9,6,8,4,4,9,6,2,8,8,6,3,9,9,4,3,
%U A155676 0,9,9,3,5,1,4,0,6,1,0,5,4,1,7,1,5,0,4,9,4,6,6,8,7,5,4,4,8
%N A155676 Decimal expansion of log_9 (21).
%e A155676 1.3856218745807111300339641535412288590332356672971217396844...
%K A155676 nonn,cons,new
%O A155676 1,2
%A A155676 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155675
%S A155675 1,4,6,4,1,0,5,8,0,7,5,9,2,9,2,0,0,9,6,2,9,8,5,6,9,4,2,0,3,9,3,2,1,5,7,
%T A155675 7,2,4,6,6,9,4,7,0,1,1,2,1,9,5,4,0,6,1,4,7,1,1,0,1,4,7,9,2,8,7,0,4,7,3,
%U A155675 0,2,5,5,5,2,1,8,3,8,4,9,6,7,3,3,8,0,4,9,1,3,6,2,7,6,6,3,4
%N A155675 Decimal expansion of log_8 (21).
%e A155675 1.4641058075929200962985694203932157724669470112195406147110...
%K A155675 nonn,cons,new
%O A155675 1,2
%A A155675 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155591
%S A155591 1,5,6,4,5,7,5,0,3,4,0,5,3,5,7,9,6,1,3,8,0,4,5,5,0,1,6,7,1,7,4,9,0,8,5,
%T A155591 3,6,1,4,3,2,2,7,9,1,1,1,8,6,7,9,2,5,9,5,0,4,5,4,0,9,2,6,2,3,0,7,7,5,2,
%U A155591 3,1,4,2,0,0,4,0,9,4,9,9,0,1,0,2,8,1,5,4,4,5,8,4,3,6,1,2,6
%N A155591 Decimal expansion of log_7 (21).
%e A155591 1.5645750340535796138045501671749085361432279111867925950454...
%K A155591 nonn,cons,new
%O A155591 1,2
%A A155591 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155554
%S A155554 1,6,9,9,1,8,0,3,2,5,2,6,7,1,5,0,2,5,6,1,1,5,7,9,5,9,1,2,4,6,0,0,0,0,4,
%T A155554 5,6,4,5,3,6,3,9,0,9,5,7,4,4,0,8,9,5,6,6,4,9,7,6,0,7,5,3,1,4,4,9,9,5,2,
%U A155554 6,2,7,3,3,1,4,2,2,8,4,7,1,5,8,6,8,9,3,6,0,8,9,4,3,2,8,0,2
%N A155554 Decimal expansion of log_6 (21).
%e A155554 1.6991803252671502561157959124600004564536390957440895664976...
%K A155554 nonn,cons,new
%O A155554 1,2
%A A155554 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155553
%S A155553 1,8,9,1,6,6,8,1,4,9,6,0,8,1,5,2,8,5,1,8,9,7,8,8,2,7,0,4,8,1,8,4,1,2,3,
%T A155553 2,4,1,4,1,2,2,5,3,2,9,5,8,4,0,0,0,3,3,8,3,6,6,2,9,2,8,9,2,3,4,6,6,2,4,
%U A155553 3,6,3,9,2,4,4,1,3,2,6,3,9,3,5,9,7,1,5,3,9,8,9,3,9,9,5,4,1
%N A155553 Decimal expansion of log_5 (21).
%e A155553 1.8916681496081528518978827048184123241412253295840003383662...
%K A155553 nonn,cons,new
%O A155553 1,2
%A A155553 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155545
%S A155545 2,1,9,6,1,5,8,7,1,1,3,8,9,3,8,0,1,4,4,4,4,7,8,5,4,1,3,0,5,8,9,8,2,3,6,
%T A155545 5,8,7,0,0,4,2,0,5,1,6,8,2,9,3,1,0,9,2,2,0,6,6,5,2,2,1,8,9,3,0,5,7,0,9,
%U A155545 5,3,8,3,2,8,2,7,5,7,7,4,5,1,0,0,7,0,7,3,7,0,4,4,1,4,9,5,1
%N A155545 Decimal expansion of log_4 (21).
%e A155545 2.1961587113893801444478541305898236587004205168293109220665...
%K A155545 nonn,cons,new
%O A155545 1,1
%A A155545 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155541
%S A155541 2,7,7,1,2,4,3,7,4,9,1,6,1,4,2,2,2,6,0,0,6,7,9,2,8,3,0,7,0,8,2,4,5,7,7,
%T A155541 1,8,0,6,6,4,7,1,3,3,4,5,9,4,2,4,3,4,7,9,3,6,8,9,9,2,5,7,7,2,7,9,8,8,6,
%U A155541 1,9,8,7,0,2,8,1,2,2,1,0,8,3,4,3,0,0,9,8,9,3,3,7,5,0,8,9,7
%N A155541 Decimal expansion of log_3 (21).
%e A155541 2.7712437491614222600679283070824577180664713345942434793689...
%K A155541 nonn,cons,new
%O A155541 1,1
%A A155541 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155536
%S A155536 4,3,9,2,3,1,7,4,2,2,7,7,8,7,6,0,2,8,8,8,9,5,7,0,8,2,6,1,1,7,9,6,4,7,3,
%T A155536 1,7,4,0,0,8,4,1,0,3,3,6,5,8,6,2,1,8,4,4,1,3,3,0,4,4,3,7,8,6,1,1,4,1,9,
%U A155536 0,7,6,6,5,6,5,5,1,5,4,9,0,2,0,1,4,1,4,7,4,0,8,8,2,9,9,0,2
%N A155536 Decimal expansion of log_2 (21).
%e A155536 4.3923174227787602888957082611796473174008410336586218441330...
%K A155536 nonn,cons,new
%O A155536 1,1
%A A155536 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155535
%S A155535 9,4,2,6,3,1,0,6,7,1,4,7,7,8,5,4,2,3,9,7,3,7,7,5,0,3,2,0,9,4,3,6,4,4,0,
%T A155535 5,2,4,6,3,4,3,3,2,7,2,7,7,1,4,8,8,2,1,5,3,8,5,0,8,3,4,1,6,4,9,2,5,9,9,
%U A155535 3,3,4,9,0,0,0,4,0,0,8,4,5,5,2,2,9,0,8,2,1,1,4,6,8,5,0,3,9
%N A155535 Decimal expansion of log_24 (20).
%e A155535 .94263106714778542397377503209436440524634332727714882153850...
%K A155535 nonn,cons,new
%O A155535 0,1
%A A155535 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155534
%S A155534 9,5,5,4,2,5,8,6,5,0,3,1,0,5,9,3,3,6,9,5,7,7,7,5,3,8,8,7,3,1,8,5,4,1,5,
%T A155534 1,9,9,9,9,2,1,2,6,3,7,6,8,4,8,0,7,2,9,2,7,7,7,9,4,8,7,1,7,7,4,1,8,9,4,
%U A155534 6,6,3,0,2,0,6,2,8,7,1,7,3,6,2,9,0,0,0,4,3,6,5,3,9,8,0,9,9
%N A155534 Decimal expansion of log_23 (20).
%e A155534 .95542586503105933695777538873185415199992126376848072927779...
%K A155534 nonn,cons,new
%O A155534 0,1
%A A155534 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155533
%S A155533 9,6,9,1,6,5,6,8,3,9,9,0,9,2,2,3,8,6,7,9,5,6,0,0,2,9,0,7,6,6,2,6,2,8,7,
%T A155533 7,8,1,9,5,3,7,4,5,0,1,6,4,2,8,8,7,9,7,6,4,8,3,2,1,8,1,2,8,7,0,2,9,1,9,
%U A155533 8,2,0,9,0,8,6,8,8,9,4,9,8,3,3,9,2,9,2,6,0,4,8,5,6,9,9,1,9
%N A155533 Decimal expansion of log_22 (20).
%e A155533 .96916568399092238679560029076626287781953745016428879764832...
%K A155533 nonn,cons,new
%O A155533 0,1
%A A155533 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155532
%S A155532 9,8,3,9,7,4,4,4,4,2,1,3,3,5,4,0,6,0,6,0,0,2,0,7,1,9,7,2,6,0,9,0,1,9,0,
%T A155532 5,3,2,1,0,9,6,3,1,3,8,1,9,3,4,6,9,7,8,7,9,3,3,2,5,5,7,4,5,0,1,6,5,5,6,
%U A155532 5,3,6,1,5,8,3,2,0,6,0,8,5,2,7,4,9,3,6,1,9,5,4,8,3,2,1,7,6
%N A155532 Decimal expansion of log_21 (20).
%e A155532 .98397444421335406060020719726090190532109631381934697879332...
%K A155532 nonn,cons,new
%O A155532 0,1
%A A155532 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155531
%S A155531 1,0,1,7,4,2,0,3,9,6,4,6,6,1,7,8,9,2,2,5,0,9,3,7,5,4,9,0,9,5,2,3,5,1,1,
%T A155531 6,1,8,7,9,2,5,0,8,0,5,8,4,8,6,8,9,1,5,2,4,7,3,6,8,3,2,1,7,8,4,2,3,2,2,
%U A155531 9,9,9,0,8,2,0,7,8,8,2,5,1,1,9,9,4,4,3,9,3,3,3,8,6,4,4,9,7
%N A155531 Decimal expansion of log_19 (20).
%e A155531 1.0174203964661789225093754909523511618792508058486891524736...
%K A155531 nonn,cons,new
%O A155531 1,4
%A A155531 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155530
%S A155530 1,0,3,6,4,5,2,2,3,6,7,6,5,0,4,3,6,0,9,4,7,0,4,3,1,3,9,9,9,3,0,8,9,5,7,
%T A155530 2,5,8,8,4,1,8,4,8,4,5,0,4,6,6,6,8,7,2,6,1,5,1,0,8,2,0,2,9,6,9,6,5,7,2,
%U A155530 2,2,9,7,8,5,9,5,1,1,6,1,2,4,8,8,5,1,8,0,1,1,5,0,3,2,5,0,6
%N A155530 Decimal expansion of log_18 (20).
%e A155530 1.0364522367650436094704313999308957258841848450466687261510...
%K A155530 nonn,cons,new
%O A155530 1,3
%A A155530 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155529
%S A155529 1,0,5,7,3,6,2,0,5,1,4,1,0,1,8,5,0,2,9,6,4,5,3,8,3,4,8,0,9,5,8,5,7,6,1,
%T A155529 3,9,6,8,6,0,2,3,9,9,5,5,9,3,1,6,8,6,0,6,4,9,5,2,3,2,7,4,8,6,1,2,5,9,7,
%U A155529 9,0,2,0,3,6,8,1,8,5,0,0,5,1,0,7,1,4,9,6,4,4,0,8,2,8,8,2,8
%N A155529 Decimal expansion of log_17 (20).
%e A155529 1.0573620514101850296453834809585761396860239955931686064952...
%K A155529 nonn,cons,new
%O A155529 1,3
%A A155529 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155528
%S A155528 1,0,8,0,4,8,2,0,2,3,7,2,1,8,4,0,5,8,6,9,6,7,5,7,9,8,5,7,3,7,2,3,4,7,5,
%T A155528 4,3,9,6,6,2,0,7,8,4,8,2,5,6,1,4,5,1,5,3,0,1,3,6,8,9,0,9,8,9,5,3,9,8,3,
%U A155528 6,9,4,1,5,2,1,5,6,3,0,3,9,6,2,5,3,4,9,3,5,8,3,9,8,4,2,5,3
%N A155528 Decimal expansion of log_16 (20).
%e A155528 1.0804820237218405869675798573723475439662078482561451530136...
%K A155528 nonn,cons,new
%O A155528 1,3
%A A155528 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155527
%S A155527 1,1,0,6,2,3,2,1,7,8,5,3,7,4,1,8,0,8,4,3,9,2,4,5,0,3,6,1,1,2,8,2,1,2,0,
%T A155527 1,1,3,1,0,0,1,5,9,8,1,2,5,1,5,2,1,8,5,7,1,1,0,6,8,3,8,3,5,6,7,8,0,6,7,
%U A155527 2,6,6,2,5,5,2,7,2,1,9,2,6,4,8,8,4,0,3,7,6,5,9,2,3,5,1,3,3
%N A155527 Decimal expansion of log_15 (20).
%e A155527 1.1062321785374180843924503611282120113100159812515218571106...
%K A155527 nonn,cons,new
%O A155527 1,4
%A A155527 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155526
%S A155526 1,1,3,5,1,5,2,4,0,4,5,8,6,3,4,9,4,3,8,0,0,3,2,2,6,3,0,7,1,7,8,0,3,1,6,
%T A155526 2,3,7,0,8,2,4,9,1,2,6,7,3,8,8,1,4,4,6,5,0,5,3,6,1,7,9,6,5,8,5,4,2,8,7,
%U A155526 6,1,4,4,0,2,1,2,0,6,1,7,4,6,9,8,4,5,1,1,9,5,3,0,6,6,2,7,4
%N A155526 Decimal expansion of log_14 (20).
%e A155526 1.1351524045863494380032263071780316237082491267388144650536...
%K A155526 nonn,cons,new
%O A155526 1,3
%A A155526 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155525
%S A155525 1,1,6,7,9,4,9,8,7,1,9,2,9,9,4,2,8,3,4,2,1,6,5,8,5,6,9,9,7,2,5,2,0,3,0,
%T A155525 0,6,8,8,3,6,5,4,5,2,9,6,4,6,9,0,6,1,7,5,1,2,3,1,5,0,5,6,0,2,1,3,9,8,7,
%U A155525 8,5,5,7,8,4,0,5,9,6,3,0,9,2,4,2,3,8,2,3,0,9,3,9,6,2,5,9,5
%N A155525 Decimal expansion of log_13 (20).
%e A155525 1.1679498719299428342165856997252030068836545296469061751231...
%K A155525 nonn,cons,new
%O A155525 1,3
%A A155525 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155524
%S A155524 1,2,0,5,5,7,1,3,5,3,6,8,0,2,5,6,6,5,9,3,0,4,0,3,7,5,0,9,2,0,4,9,7,8,6,
%T A155524 0,7,1,0,6,3,3,0,2,0,0,1,3,0,4,5,4,6,2,7,5,0,4,0,5,7,0,5,2,6,7,0,7,5,8,
%U A155524 9,9,1,0,4,3,1,4,1,8,3,4,2,9,0,3,1,6,9,3,5,3,8,5,2,2,5,9,2
%N A155524 Decimal expansion of log_12 (20).
%e A155524 1.2055713536802566593040375092049786071063302001304546275040...
%K A155524 nonn,cons,new
%O A155524 1,2
%A A155524 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155523
%S A155523 1,2,4,9,3,1,7,3,9,4,1,0,7,0,1,5,3,5,6,6,7,2,3,2,2,6,5,2,7,1,9,5,2,3,9,
%T A155523 5,5,8,6,7,5,7,4,9,3,4,3,8,4,3,9,9,8,7,6,8,4,9,5,9,2,7,5,5,4,7,0,6,1,0,
%U A155523 0,3,2,7,6,5,3,2,0,5,7,5,0,8,5,8,8,1,2,9,7,7,0,6,8,1,1,4,1
%N A155523 Decimal expansion of log_11 (20).
%e A155523 1.2493173941070153566723226527195239558675749343843998768495...
%K A155523 nonn,cons,new
%O A155523 1,2
%A A155523 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155522
%S A155522 1,3,0,1,0,2,9,9,9,5,6,6,3,9,8,1,1,9,5,2,1,3,7,3,8,8,9,4,7,2,4,4,9,3,0,
%T A155522 2,6,7,6,8,1,8,9,8,8,1,4,6,2,1,0,8,5,4,1,3,1,0,4,2,7,4,6,1,1,2,7,1,0,8,
%U A155522 1,8,9,2,7,4,4,2,4,5,0,9,4,8,6,9,2,7,2,5,2,1,1,8,1,8,6,1,7
%N A155522 Decimal expansion of log_10 (20).
%e A155522 1.3010299956639811952137388947244930267681898814621085413104...
%K A155522 nonn,cons,new
%O A155522 1,2
%A A155522 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155503
%S A155503 1,3,6,3,4,1,6,5,1,3,9,3,0,4,2,1,0,2,0,6,9,8,0,4,7,3,1,8,1,8,2,0,8,1,0,
%T A155503 5,2,4,5,3,5,5,1,8,2,3,4,6,4,9,0,5,2,7,2,3,9,7,1,0,0,1,4,1,2,3,6,4,3,1,
%U A155503 3,3,9,4,7,6,4,2,7,7,1,6,8,8,8,9,6,9,2,4,5,4,2,9,2,1,6,4,9
%N A155503 Decimal expansion of log_9 (20).
%e A155503 1.3634165139304210206980473181820810524535518234649052723971...
%K A155503 nonn,cons,new
%O A155503 1,2
%A A155503 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155502
%S A155502 1,4,4,0,6,4,2,6,9,8,2,9,5,7,8,7,4,4,9,2,9,0,1,0,6,4,7,6,4,9,6,4,6,3,3,
%T A155502 9,1,9,5,4,9,4,3,7,9,7,6,7,4,8,6,0,2,0,4,0,1,8,2,5,2,1,3,1,9,3,8,6,4,4,
%U A155502 9,2,5,5,3,6,2,0,8,4,0,5,2,8,3,3,7,9,9,1,4,4,5,3,1,2,3,3,8
%N A155502 Decimal expansion of log_8 (20).
%e A155502 1.4406426982957874492901064764964633919549437976748602040182...
%K A155502 nonn,cons,new
%O A155502 1,2
%A A155502 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155496
%S A155496 1,5,3,9,5,0,1,8,4,9,5,6,2,9,6,0,5,0,3,3,3,2,1,0,5,6,3,9,6,4,8,1,4,9,6,
%T A155496 7,7,4,6,3,2,0,1,6,8,5,7,1,5,2,0,8,4,2,3,3,9,5,9,1,7,3,6,8,2,4,6,7,7,9,
%U A155496 4,5,6,9,0,7,7,1,9,4,4,6,6,3,7,3,7,2,2,2,7,3,5,2,0,5,4,2,2
%N A155496 Decimal expansion of log_7 (20).
%e A155496 1.5395018495629605033321056396481496774632016857152084233959...
%K A155496 nonn,cons,new
%O A155496 1,2
%A A155496 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155490
%S A155490 1,6,7,1,9,5,0,0,1,6,1,7,3,0,1,0,3,4,6,8,1,3,7,2,5,2,3,5,0,2,2,1,1,0,4,
%T A155490 2,5,1,8,0,8,7,5,0,7,2,7,3,8,8,5,4,6,5,6,2,5,9,6,8,8,8,4,6,8,9,6,6,3,5,
%U A155490 2,1,2,1,5,7,5,8,5,2,3,7,9,7,7,9,8,5,2,9,7,3,5,5,8,0,1,4,8
%N A155490 Decimal expansion of log_6 (20).
%e A155490 1.6719500161730103468137252350221104251808750727388546562596...
%K A155490 nonn,cons,new
%O A155490 1,2
%A A155490 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155184
%S A155184 1,8,6,1,3,5,3,1,1,6,1,4,6,7,8,6,1,0,1,3,4,0,2,1,3,1,3,7,5,2,7,9,3,1,2,
%T A155184 6,4,1,3,9,5,8,3,8,6,4,1,5,9,5,2,0,8,9,8,6,4,3,9,5,2,0,7,5,9,2,1,3,2,4,
%U A155184 1,6,5,0,7,5,7,7,1,0,1,2,1,6,7,3,9,6,1,9,8,8,9,0,5,3,3,9,5
%N A155184 Decimal expansion of log_5 (20).
%e A155184 1.8613531161467861013402131375279312641395838641595208986439...
%K A155184 nonn,cons,new
%O A155184 1,2
%A A155184 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155183
%S A155183 2,1,6,0,9,6,4,0,4,7,4,4,3,6,8,1,1,7,3,9,3,5,1,5,9,7,1,4,7,4,4,6,9,5,0,
%T A155183 8,7,9,3,2,4,1,5,6,9,6,5,1,2,2,9,0,3,0,6,0,2,7,3,7,8,1,9,7,9,0,7,9,6,7,
%U A155183 3,8,8,3,0,4,3,1,2,6,0,7,9,2,5,0,6,9,8,7,1,6,7,9,6,8,5,0,7
%N A155183 Decimal expansion of log_4 (20).
%e A155183 2.1609640474436811739351597147446950879324156965122903060273...
%K A155183 nonn,cons,new
%O A155183 1,1
%A A155183 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155172
%S A155172 4,3,2,1,9,2,8,0,9,4,8,8,7,3,6,2,3,4,7,8,7,0,3,1,9,4,2,9,4,8,9,3,9,0,1,
%T A155172 7,5,8,6,4,8,3,1,3,9,3,0,2,4,5,8,0,6,1,2,0,5,4,7,5,6,3,9,5,8,1,5,9,3,4,
%U A155172 7,7,6,6,0,8,6,2,5,2,1,5,8,5,0,1,3,9,7,4,3,3,5,9,3,7,0,1,5
%N A155172 Decimal expansion of log_2 (20).
%e A155172 4.3219280948873623478703194294893901758648313930245806120547...
%K A155172 nonn,cons,new
%O A155172 1,1
%A A155172 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155168
%S A155168 9,2,6,4,9,1,2,2,2,7,2,5,4,7,2,8,0,8,4,3,8,9,8,1,1,0,2,2,3,9,6,0,5,4,3,
%T A155168 8,8,8,3,0,0,2,6,7,2,2,1,6,3,2,4,5,0,1,5,7,2,2,7,5,7,7,1,6,0,7,4,9,1,2,
%U A155168 0,5,2,7,3,4,6,3,4,2,7,6,9,4,4,7,0,4,3,7,0,8,3,1,9,4,2,4,2
%N A155168 Decimal expansion of log_24 (19).
%e A155168 .92649122272547280843898110223960543888300267221632450157227...
%K A155168 nonn,cons,new
%O A155168 0,1
%A A155168 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155166
%S A155166 9,3,9,0,6,6,9,4,6,5,1,4,4,9,2,8,3,4,7,4,7,0,2,4,0,5,5,8,6,0,2,0,6,3,4,
%T A155166 2,4,0,8,2,4,7,2,9,8,3,0,2,8,5,0,1,6,3,9,3,1,0,2,3,8,8,3,4,8,7,9,0,6,9,
%U A155166 8,3,5,7,9,9,9,5,7,9,3,4,9,3,0,1,5,5,0,1,1,3,4,7,2,9,0,1,8
%N A155166 Decimal expansion of log_23 (19).
%e A155166 .93906694651449283474702405586020634240824729830285016393102...
%K A155166 nonn,cons,new
%O A155166 0,1
%A A155166 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155165
%S A155165 9,5,2,5,7,1,5,1,0,6,1,3,6,4,5,7,1,5,0,0,5,5,0,3,7,7,4,0,4,5,6,5,9,4,2,
%T A155165 3,4,5,6,9,4,1,3,2,9,3,8,6,2,4,0,7,8,5,1,5,3,6,4,6,4,2,5,3,1,5,7,3,7,3,
%U A155165 4,3,6,6,3,6,5,6,3,7,1,4,4,0,6,0,3,0,2,8,4,4,8,3,6,1,2,4,0
%N A155165 Decimal expansion of log_22 (19).
%e A155165 .95257151061364571500550377404565942345694132938624078515364...
%K A155165 nonn,cons,new
%O A155165 0,1
%A A155165 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155129
%S A155129 9,6,7,1,2,6,7,1,3,4,3,2,3,3,0,2,5,9,0,8,6,2,2,5,2,7,0,3,1,0,3,6,4,0,6,
%T A155129 2,1,0,6,9,6,6,3,3,3,3,9,8,2,2,3,0,6,7,6,7,7,4,6,7,4,0,8,2,2,0,0,3,0,1,
%U A155129 3,5,7,6,5,0,8,3,9,1,6,0,7,3,2,9,0,3,4,8,9,7,1,3,9,6,1,2,3
%N A155129 Decimal expansion of log_21 (19).
%e A155129 .96712671343233025908622527031036406210696633339822306767746...
%K A155129 nonn,cons,new
%O A155129 0,1
%A A155129 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155115
%S A155115 9,8,2,8,7,7,8,7,7,6,9,2,7,5,5,6,7,9,7,4,6,4,5,6,9,4,8,8,6,4,2,9,9,2,4,
%T A155115 0,5,9,8,0,7,1,5,4,9,5,0,4,1,3,2,1,8,6,2,8,8,5,0,7,0,9,8,6,9,8,1,4,8,6,
%U A155115 2,6,6,1,0,5,2,2,5,0,8,3,1,9,6,1,1,7,2,0,0,0,6,6,0,2,3,9,8
%N A155115 Decimal expansion of log_20 (19).
%e A155115 .98287787769275567974645694886429924059807154950413218628850...
%K A155115 nonn,cons,new
%O A155115 0,1
%A A155115 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155094
%S A155094 1,0,1,8,7,0,5,9,7,4,8,0,1,5,3,5,5,8,4,4,9,3,6,1,8,2,3,2,0,8,0,7,2,8,9,
%T A155094 9,9,6,1,1,8,7,1,7,3,4,5,3,5,1,6,7,8,7,9,7,2,8,1,5,3,9,2,4,0,2,7,0,7,1,
%U A155094 8,2,8,9,4,3,3,7,2,2,4,0,3,7,5,6,6,9,6,8,4,8,1,1,3,9,5,1,1
%N A155094 Decimal expansion of log_18 (19).
%e A155094 1.0187059748015355844936182320807289996118717345351678797281...
%K A155094 nonn,cons,new
%O A155094 1,4
%A A155094 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155080
%S A155080 1,0,3,9,2,5,7,7,6,9,0,4,2,9,0,1,0,8,4,7,7,7,8,0,7,4,6,7,0,8,3,6,0,1,0,
%T A155080 3,5,0,9,9,7,2,1,1,8,1,2,2,2,6,5,5,8,2,5,0,2,1,7,6,7,1,1,7,8,9,0,7,0,4,
%U A155080 9,3,0,4,3,2,0,7,8,1,4,0,3,7,3,5,2,5,7,7,8,4,0,8,2,6,8,0,1
%N A155080 Decimal expansion of log_17 (19).
%e A155080 1.0392577690429010847778074670836010350997211812226558250217...
%K A155080 nonn,cons,new
%O A155080 1,3
%A A155080 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155079
%S A155079 1,0,6,1,9,8,1,8,7,8,3,6,0,8,9,6,3,7,3,4,4,8,3,7,9,8,5,5,7,2,6,7,0,8,6,
%T A155079 0,5,6,7,3,3,7,6,8,9,2,4,1,5,3,8,3,5,0,3,6,4,5,3,8,1,1,8,2,7,1,6,1,4,1,
%U A155079 3,0,2,0,5,1,3,6,6,2,2,1,7,0,0,6,7,7,0,1,3,5,4,3,0,4,4,1,2
%N A155079 Decimal expansion of log_16 (19).
%e A155079 1.0619818783608963734483798557267086056733768924153835036453...
%K A155079 nonn,cons,new
%O A155079 1,3
%A A155079 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155068
%S A155068 1,0,8,7,2,9,1,1,3,5,8,7,6,2,9,1,0,7,6,6,4,9,1,5,1,4,3,4,4,6,0,2,9,9,4,
%T A155068 3,7,7,9,0,0,9,3,9,0,0,2,8,0,7,1,2,5,2,4,9,5,1,0,2,2,9,8,0,8,4,8,5,0,3,
%U A155068 2,9,1,4,1,3,0,2,8,7,7,2,4,1,1,3,6,2,8,1,1,9,2,5,9,8,7,7,9
%N A155068 Decimal expansion of log_15 (19).
%e A155068 1.0872911358762910766491514344602994377900939002807125249510...
%K A155068 nonn,cons,new
%O A155068 1,3
%A A155068 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155066
%S A155066 1,1,1,5,7,1,6,1,8,6,2,7,7,6,5,9,4,7,4,4,5,9,7,9,5,8,1,1,4,2,8,3,8,5,9,
%T A155066 9,3,1,6,9,4,6,6,8,5,5,0,2,5,9,6,9,6,8,6,0,6,3,2,5,9,8,6,9,7,7,6,6,7,5,
%U A155066 7,3,2,1,0,6,5,1,4,1,5,3,3,0,5,3,9,1,0,6,3,5,1,6,2,8,4,3,1
%N A155066 Decimal expansion of log_14 (19).
%e A155066 1.1157161862776594744597958114283859931694668550259696860632...
%K A155066 nonn,cons,new
%O A155066 1,4
%A A155066 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155065
%S A155065 1,1,4,7,9,5,2,0,9,1,3,7,4,0,2,8,0,1,3,0,6,4,7,7,5,5,9,7,1,1,0,6,3,6,4,
%T A155065 5,9,4,8,4,0,9,2,9,1,9,4,4,9,7,6,6,6,1,2,3,2,9,1,4,5,0,3,2,5,2,3,0,0,4,
%U A155065 6,5,2,2,4,6,9,6,7,8,1,5,1,9,3,6,6,0,8,4,6,0,5,7,8,4,1,4,8
%N A155065 Decimal expansion of log_13 (19).
%e A155065 1.1479520913740280130647755971106364594840929194497666123291...
%K A155065 nonn,cons,new
%O A155065 1,3
%A A155065 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155064
%S A155064 1,1,8,4,9,2,9,4,1,3,5,1,2,4,3,3,2,0,4,7,1,3,4,8,7,1,4,9,7,9,2,5,6,4,8,
%T A155064 6,2,5,4,7,2,5,3,2,4,9,8,8,5,0,6,0,4,2,9,1,2,3,9,8,4,5,5,9,1,8,3,2,6,1,
%U A155064 4,8,5,8,6,3,0,5,9,3,2,6,4,1,6,0,5,9,7,7,1,0,8,3,1,0,8,9,7
%N A155064 Decimal expansion of log_12 (19).
%e A155064 1.1849294135124332047134871497925648625472532498850604291239...
%K A155064 nonn,cons,new
%O A155064 1,3
%A A155064 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155063
%S A155063 1,2,2,7,9,2,6,4,2,8,8,8,4,5,4,7,2,8,5,1,4,6,1,6,7,9,4,5,8,0,7,1,5,5,9,
%T A155063 8,5,5,0,8,9,6,7,2,0,3,8,2,6,5,0,5,5,6,5,9,1,1,1,3,3,3,2,6,1,6,7,4,9,6,
%U A155063 2,6,6,7,3,7,5,6,8,7,2,8,0,1,2,8,0,9,5,3,4,5,9,0,6,1,5,9,1
%N A155063 Decimal expansion of log_11 (19).
%e A155063 1.2279264288845472851461679458071559855089672038265055659111...
%K A155063 nonn,cons,new
%O A155063 1,2
%A A155063 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155062
%S A155062 1,2,7,8,7,5,3,6,0,0,9,5,2,8,2,8,9,6,1,5,3,6,3,3,3,4,7,5,7,5,6,9,2,9,3,
%T A155062 1,7,9,5,1,1,2,9,3,3,7,3,9,4,4,9,7,5,9,8,9,0,6,8,1,8,8,6,8,7,0,7,7,5,0,
%U A155062 8,4,1,3,5,0,6,4,2,7,2,2,8,9,4,3,8,4,4,2,0,9,0,0,2,0,5,9,0
%N A155062 Decimal expansion of log_10 (19).
%e A155062 1.2787536009528289615363334757569293179511293373944975989068...
%K A155062 nonn,cons,new
%O A155062 1,2
%A A155062 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155061
%S A155061 1,3,4,0,0,7,1,9,2,9,6,2,3,1,8,7,6,7,2,4,2,5,2,8,3,3,1,0,1,0,9,5,9,7,5,
%T A155061 6,5,2,3,3,0,7,1,4,2,1,3,4,7,1,7,6,6,1,0,9,1,8,4,4,4,2,7,8,2,5,8,9,7,0,
%U A155061 4,3,5,8,6,7,5,1,4,6,5,4,9,3,8,6,3,7,2,3,8,4,2,4,8,7,7,8,6
%N A155061 Decimal expansion of log_9 (19).
%e A155061 1.3400719296231876724252833101095975652330714213471766109184...
%K A155061 nonn,cons,new
%O A155061 1,2
%A A155061 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155060
%S A155060 1,4,1,5,9,7,5,8,3,7,8,1,4,5,2,8,4,9,7,9,3,1,1,7,3,1,4,0,9,6,8,9,4,4,8,
%T A155060 0,7,5,6,4,5,0,2,5,2,3,2,2,0,5,1,1,3,3,8,1,9,3,8,4,1,5,7,6,9,5,4,8,5,5,
%U A155060 0,6,9,4,0,1,8,2,1,6,2,8,9,3,4,2,3,6,0,1,8,0,5,7,3,9,2,1,7
%N A155060 Decimal expansion of log_8 (19).
%e A155060 1.4159758378145284979311731409689448075645025232205113381938...
%K A155060 nonn,cons,new
%O A155060 1,2
%A A155060 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155059
%S A155059 1,5,1,3,1,4,2,3,1,0,6,0,2,5,1,4,6,4,7,6,1,4,8,2,7,8,2,7,1,6,8,8,2,7,8,
%T A155059 9,7,4,9,5,8,7,0,4,2,7,3,8,1,1,3,5,7,3,1,6,0,4,4,8,3,4,6,8,1,8,1,4,2,2,
%U A155059 8,4,6,5,2,7,4,6,7,4,1,3,4,0,5,8,7,0,5,7,2,0,1,6,1,6,2,0,6
%N A155059 Decimal expansion of log_7 (19).
%e A155059 1.5131423106025146476148278271688278974958704273811357316044...
%K A155059 nonn,cons,new
%O A155059 1,2
%A A155059 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155044
%S A155044 1,6,4,3,3,2,2,6,8,3,5,0,4,4,9,6,9,4,4,3,3,1,3,4,1,4,4,5,4,6,6,9,4,6,7,
%T A155044 2,7,2,1,9,7,8,3,6,7,1,6,7,9,4,1,9,4,1,8,6,1,3,7,1,3,5,3,4,4,8,7,9,4,7,
%U A155044 7,9,6,2,6,7,6,9,5,0,9,7,9,2,8,2,7,3,8,1,0,5,0,9,1,4,5,6,1
%N A155044 Decimal expansion of log_6 (19).
%e A155044 1.6433226835044969443313414454669467272197836716794194186137...
%K A155044 nonn,cons,new
%O A155044 1,2
%A A155044 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155035
%S A155035 1,8,2,9,4,8,2,8,0,0,4,3,5,1,5,0,4,8,6,8,8,2,8,2,8,1,8,0,4,8,0,6,4,9,8,
%T A155035 2,9,1,7,8,0,7,8,3,3,0,9,1,0,6,7,8,3,8,4,0,7,4,6,1,1,5,5,5,8,1,1,5,2,5,
%U A155035 6,3,9,2,8,6,9,8,4,3,9,1,2,6,2,3,9,4,5,0,3,4,7,4,9,4,6,9,3
%N A155035 Decimal expansion of log_5 (19).
%e A155035 1.8294828004351504868828281804806498291780783309106783840746...
%K A155035 nonn,cons,new
%O A155035 1,2
%A A155035 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155004
%S A155004 2,1,2,3,9,6,3,7,5,6,7,2,1,7,9,2,7,4,6,8,9,6,7,5,9,7,1,1,4,5,3,4,1,7,2,
%T A155004 1,1,3,4,6,7,5,3,7,8,4,8,3,0,7,6,7,0,0,7,2,9,0,7,6,2,3,6,5,4,3,2,2,8,2,
%U A155004 6,0,4,1,0,2,7,3,2,4,4,3,4,0,1,3,5,4,0,2,7,0,8,6,0,8,8,2,5
%N A155004 Decimal expansion of log_4 (19).
%e A155004 2.1239637567217927468967597114534172113467537848307670072907...
%K A155004 nonn,cons,new
%O A155004 1,1
%A A155004 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A155003
%S A155003 2,6,8,0,1,4,3,8,5,9,2,4,6,3,7,5,3,4,4,8,5,0,5,6,6,6,2,0,2,1,9,1,9,5,1,
%T A155003 3,0,4,6,6,1,4,2,8,4,2,6,9,4,3,5,3,2,2,1,8,3,6,8,8,8,5,5,6,5,1,7,9,4,0,
%U A155003 8,7,1,7,3,5,0,2,9,3,0,9,8,7,7,2,7,4,4,7,6,8,4,9,7,5,5,7,3
%N A155003 Decimal expansion of log_3 (19).
%e A155003 2.6801438592463753448505666202191951304661428426943532218368...
%K A155003 nonn,cons,new
%O A155003 1,1
%A A155003 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154995
%S A154995 4,2,4,7,9,2,7,5,1,3,4,4,3,5,8,5,4,9,3,7,9,3,5,1,9,4,2,2,9,0,6,8,3,4,4,
%T A154995 2,2,6,9,3,5,0,7,5,6,9,6,6,1,5,3,4,0,1,4,5,8,1,5,2,4,7,3,0,8,6,4,5,6,5,
%U A154995 2,0,8,2,0,5,4,6,4,8,8,6,8,0,2,7,0,8,0,5,4,1,7,2,1,7,6,5,1
%N A154995 Decimal expansion of log_2 (19).
%e A154995 4.2479275134435854937935194229068344226935075696615340145815...
%K A154995 nonn,cons,new
%O A154995 1,1
%A A154995 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154994
%S A154994 9,0,9,4,7,8,5,4,0,0,7,2,3,4,2,2,0,3,8,5,3,3,1,0,9,6,7,7,8,3,0,5,8,0,5,
%T A154994 6,8,6,1,6,9,7,8,7,2,5,0,2,5,0,1,1,6,1,9,2,6,3,0,9,2,1,7,6,7,9,0,7,8,8,
%U A154994 0,9,2,4,9,5,0,3,8,2,4,5,1,0,0,4,1,1,4,2,9,0,5,8,8,8,9,2,8
%N A154994 Decimal expansion of log_24 (18).
%e A154994 .90947854007234220385331096778305805686169787250250116192630...
%K A154994 nonn,cons,new
%O A154994 0,1
%A A154994 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154993
%S A154993 9,2,1,8,2,3,3,4,2,3,0,1,9,2,5,7,0,0,9,6,3,0,4,2,8,7,1,3,8,3,3,7,6,3,7,
%T A154993 8,5,5,9,7,3,8,8,0,8,7,0,6,8,3,3,3,3,8,0,1,6,3,1,0,5,7,3,9,3,4,7,9,5,4,
%U A154993 4,0,4,7,2,5,7,6,2,4,6,7,7,7,2,7,4,0,4,0,3,8,0,7,3,7,5,6,5
%N A154993 Decimal expansion of log_23 (18).
%e A154993 .92182334230192570096304287138337637855973880870683333801631...
%K A154993 nonn,cons,new
%O A154993 0,1
%A A154993 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154978
%S A154978 9,3,5,0,7,9,9,2,9,0,2,3,9,0,2,9,0,4,4,3,8,1,3,4,4,7,9,9,6,7,8,0,9,2,4,
%T A154978 5,9,3,8,2,6,9,5,6,6,1,0,4,6,5,5,4,8,2,3,3,8,1,8,8,1,6,6,8,4,6,4,3,1,9,
%U A154978 6,6,0,7,0,5,8,7,6,4,6,6,6,8,7,9,0,8,6,0,4,4,0,9,3,3,1,3,3
%N A154978 Decimal expansion of log_22 (18).
%e A154978 .93507992902390290443813447996780924593826956610465548233818...
%K A154978 nonn,cons,new
%O A154978 0,1
%A A154978 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154977
%S A154977 9,4,9,3,6,7,8,6,2,1,2,6,0,1,3,3,4,4,4,7,2,2,4,3,5,6,5,1,0,9,5,0,1,5,1,
%T A154977 5,7,6,9,8,3,8,5,5,0,7,3,8,8,3,8,5,9,1,4,8,6,2,5,1,2,3,0,8,3,8,5,4,8,5,
%U A154977 8,0,6,1,9,4,0,6,7,2,5,3,8,3,6,7,0,6,5,9,2,6,0,9,2,0,5,9,0
%N A154977 Decimal expansion of log_21 (18).
%e A154977 .94936786212601334447224356510950151576983855073883859148625...
%K A154977 nonn,cons,new
%O A154977 0,1
%A A154977 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154976
%S A154976 9,6,4,8,2,9,7,9,5,8,4,3,9,2,8,4,3,2,0,8,9,3,1,1,9,8,6,4,1,6,3,0,5,8,0,
%T A154976 3,0,8,2,5,0,2,3,6,9,2,3,8,2,2,9,9,9,8,4,1,7,5,9,2,9,4,8,6,6,3,4,1,7,9,
%U A154976 4,7,8,9,3,2,9,6,6,0,3,4,7,1,5,7,7,4,5,9,6,1,3,5,6,6,7,5,6
%N A154976 Decimal expansion of log_20 (18).
%e A154976 .96482979584392843208931198641630580308250236923822999841759...
%K A154976 nonn,cons,new
%O A154976 0,1
%A A154976 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154975
%S A154975 9,8,1,6,3,7,5,1,3,4,0,9,9,1,2,1,3,4,2,0,3,4,3,0,1,9,6,2,4,7,2,2,7,9,2,
%T A154975 6,2,8,6,6,4,0,2,7,3,1,3,2,0,8,8,7,6,3,2,6,5,8,6,4,8,5,2,3,9,6,6,1,7,6,
%U A154975 8,5,5,7,8,1,4,9,1,1,5,8,0,0,5,0,0,1,4,5,7,0,8,1,6,3,9,7,6
%N A154975 Decimal expansion of log_19 (18).
%e A154975 .98163751340991213420343019624722792628664027313208876326586...
%K A154975 nonn,cons,new
%O A154975 0,1
%A A154975 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154974
%S A154974 1,0,2,0,1,7,4,4,1,2,1,9,5,2,0,6,1,8,1,2,6,2,1,6,0,2,1,2,7,0,0,8,1,5,1,
%T A154974 0,1,0,5,5,6,0,8,2,2,4,4,9,6,1,1,6,1,8,2,4,7,9,8,6,6,8,2,3,1,0,8,8,1,5,
%U A154974 9,3,6,7,4,3,7,5,8,8,0,0,0,5,8,0,5,8,1,7,3,2,0,0,5,6,3,1,3
%N A154974 Decimal expansion of log_17 (18).
%e A154974 1.0201744121952061812621602127008151010556082244961161824798...
%K A154974 nonn,cons,new
%O A154974 1,3
%A A154974 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154973
%S A154973 1,0,4,2,4,8,1,2,5,0,3,6,0,5,7,8,0,9,0,7,2,6,8,6,9,4,7,1,9,7,3,9,0,8,2,
%T A154973 5,4,3,7,9,9,0,7,2,0,3,8,4,6,2,4,0,5,3,0,2,2,7,8,7,6,3,2,7,2,7,0,5,4,9,
%U A154973 1,1,3,8,9,7,1,7,9,2,8,1,2,6,1,1,4,0,2,3,7,4,5,9,0,4,4,1,2
%N A154973 Decimal expansion of log_16 (18).
%e A154973 1.0424812503605780907268694719739082543799072038462405302278...
%K A154973 nonn,cons,new
%O A154973 1,3
%A A154973 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154972
%S A154972 1,0,6,7,3,2,5,7,6,6,9,7,4,2,4,1,2,7,8,1,5,3,4,8,7,6,7,2,0,6,7,5,8,7,3,
%T A154972 2,9,4,0,4,6,7,7,4,3,6,2,9,1,4,6,1,9,9,7,1,2,1,2,0,9,4,8,3,2,9,1,9,6,1,
%U A154972 5,6,6,3,5,0,3,1,8,0,8,7,2,7,5,9,5,7,1,6,6,0,8,0,0,6,1,3,1
%N A154972 Decimal expansion of log_15 (18).
%e A154972 1.0673257669742412781534876720675873294046774362914619971212...
%K A154972 nonn,cons,new
%O A154972 1,3
%A A154972 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154971
%S A154971 1,0,9,5,2,2,8,8,6,2,7,6,8,7,9,1,9,7,7,0,5,1,9,8,8,2,5,3,2,5,0,1,8,4,1,
%T A154971 7,8,5,7,4,2,5,9,5,8,2,1,5,5,7,5,1,6,4,3,3,8,4,8,5,5,0,4,1,4,3,5,8,9,5,
%U A154971 5,4,0,3,5,1,7,3,7,3,1,4,0,8,3,9,9,3,0,3,7,0,2,1,5,4,9,2,2
%N A154971 Decimal expansion of log_14 (18).
%e A154971 1.0952288627687919770519882532501841785742595821557516433848...
%K A154971 nonn,cons,new
%O A154971 1,3
%A A154971 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154970
%S A154970 1,1,2,6,8,7,2,8,3,6,4,9,0,1,0,9,1,0,3,2,7,5,6,5,6,7,5,9,2,9,2,5,7,1,4,
%T A154970 4,8,2,1,1,9,0,6,0,5,9,0,8,1,0,5,0,3,8,3,4,0,2,4,2,3,6,1,8,6,5,2,2,3,9,
%U A154970 9,3,8,7,8,1,2,6,0,1,9,4,7,0,0,5,5,5,9,3,7,0,0,2,4,7,8,7,3
%N A154970 Decimal expansion of log_13 (18).
%e A154970 1.1268728364901091032756567592925714482119060590810503834024...
%K A154970 nonn,cons,new
%O A154970 1,3
%A A154970 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154969
%S A154969 1,1,6,3,1,7,1,1,6,3,0,4,6,6,1,0,4,7,0,4,2,6,8,6,7,7,5,6,8,8,6,3,4,3,1,
%T A154969 9,0,6,8,5,6,1,6,9,8,7,2,1,0,5,8,0,7,9,6,0,8,1,9,1,1,9,8,9,7,7,5,1,7,0,
%U A154969 4,8,4,2,7,8,5,9,7,3,2,2,7,5,7,9,0,8,3,4,7,9,4,8,9,1,0,6,5
%N A154969 Decimal expansion of log_12 (18).
%e A154969 1.1631711630466104704268677568863431906856169872105807960819...
%K A154969 nonn,cons,new
%O A154969 1,3
%A A154969 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154954
%S A154954 1,2,0,5,3,7,8,6,4,6,3,0,0,5,4,0,3,0,4,2,3,0,6,4,7,4,7,5,4,8,5,7,6,8,8,
%T A154954 0,4,0,4,0,5,3,3,3,8,7,2,3,5,3,3,0,6,6,0,9,5,0,9,8,0,5,1,2,2,5,3,1,2,9,
%U A154954 1,8,8,8,0,5,9,3,8,3,0,0,8,2,1,8,8,9,1,8,8,5,0,8,3,6,8,8,4
%N A154954 Decimal expansion of log_11 (18).
%e A154954 1.2053786463005403042306474754857688040405333872353306609509...
%K A154954 nonn,cons,new
%O A154954 1,2
%A A154954 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154953
%S A154953 1,2,5,5,2,7,2,5,0,5,1,0,3,3,0,6,0,6,9,8,0,3,7,9,4,7,0,1,2,3,4,7,2,3,6,
%T A154953 4,5,1,6,8,4,4,7,6,0,9,8,4,3,5,0,0,2,7,0,9,7,0,1,5,8,7,4,1,7,3,7,5,6,6,
%U A154953 4,9,4,8,4,1,7,4,6,7,5,5,5,7,2,8,6,3,9,6,3,4,1,3,4,1,8,7,7
%N A154953 Decimal expansion of log_10 (18).
%e A154953 1.2552725051033060698037947012347236451684476098435002709701...
%K A154953 nonn,cons,new
%O A154953 1,2
%A A154953 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154947
%S A154947 1,3,1,5,4,6,4,8,7,6,7,8,5,7,2,8,7,1,8,5,4,9,7,6,3,5,5,7,1,7,1,3,8,0,4,
%T A154947 2,7,1,4,9,7,9,2,8,2,0,0,6,5,9,4,0,2,1,3,9,3,5,3,2,7,4,7,1,9,1,9,3,4,2,
%U A154947 6,0,0,6,9,0,4,5,7,4,0,2,5,3,0,5,8,6,3,4,4,2,7,4,7,2,5,8,7
%N A154947 Decimal expansion of log_9 (18).
%e A154947 1.3154648767857287185497635571713804271497928200659402139353...
%K A154947 nonn,cons,new
%O A154947 1,2
%A A154947 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154927
%S A154927 1,3,8,9,9,7,5,0,0,0,4,8,0,7,7,0,7,8,7,6,3,5,8,2,5,9,6,2,6,3,1,8,7,7,6,
%T A154927 7,2,5,0,6,5,4,2,9,3,8,4,6,1,6,5,4,0,4,0,3,0,3,8,3,5,1,0,3,0,2,7,3,9,8,
%U A154927 8,1,8,5,2,9,5,7,2,3,7,5,0,1,4,8,5,3,6,4,9,9,4,5,3,9,2,1,6
%N A154927 Decimal expansion of log_8 (18).
%e A154927 1.3899750004807707876358259626318776725065429384616540403038...
%K A154927 nonn,cons,new
%O A154927 1,2
%A A154927 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154912
%S A154912 1,4,8,5,3,5,7,2,5,5,2,1,5,1,8,1,4,0,4,1,2,3,2,7,7,4,1,2,3,5,1,1,0,7,6,
%T A154912 0,1,5,8,4,2,1,2,9,8,5,1,4,6,3,9,8,8,9,0,1,3,0,3,9,4,9,8,2,4,0,6,3,7,2,
%U A154912 2,0,8,7,6,0,0,7,8,3,4,2,6,8,4,4,3,7,1,5,4,7,1,8,4,9,5,3,8
%N A154912 Decimal expansion of log_7 (18).
%e A154912 1.4853572552151814041232774123511076015842129851463988901303...
%K A154912 nonn,cons,new
%O A154912 1,2
%A A154912 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154911
%S A154911 1,6,1,3,1,4,7,1,9,2,7,6,5,4,5,8,4,1,3,1,2,9,7,5,3,8,6,1,5,3,2,1,7,9,1,
%T A154911 2,3,5,3,4,8,5,8,1,4,0,5,4,2,8,9,6,5,7,1,6,1,0,5,0,5,0,7,1,1,7,3,3,5,7,
%U A154911 9,8,1,4,5,9,2,7,7,1,9,6,1,6,8,3,4,7,6,9,9,7,0,5,1,8,3,9,9
%N A154911 Decimal expansion of log_6 (18).
%e A154911 1.6131471927654584131297538615321791235348581405428965716105...
%K A154911 nonn,cons,new
%O A154911 1,2
%A A154911 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154910
%S A154910 1,7,9,5,8,8,8,9,4,7,0,4,5,3,6,3,6,4,0,9,3,9,2,3,9,2,8,7,3,0,6,0,7,0,1,
%T A154910 3,8,1,1,9,1,3,0,7,3,1,8,2,6,0,9,4,8,6,8,6,4,2,0,8,9,4,2,0,9,4,8,1,5,4,
%U A154910 4,0,8,3,9,1,7,1,2,0,6,0,7,5,7,6,0,6,5,4,1,2,8,9,9,0,7,4,5
%N A154910 Decimal expansion of log_5 (18).
%e A154910 1.7958889470453636409392392873060701381191307318260948686420...
%K A154910 nonn,cons,new
%O A154910 1,2
%A A154910 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154909
%S A154909 2,0,8,4,9,6,2,5,0,0,7,2,1,1,5,6,1,8,1,4,5,3,7,3,8,9,4,3,9,4,7,8,1,6,5,
%T A154909 0,8,7,5,9,8,1,4,4,0,7,6,9,2,4,8,1,0,6,0,4,5,5,7,5,2,6,5,4,5,4,1,0,9,8,
%U A154909 2,2,7,7,9,4,3,5,8,5,6,2,5,2,2,2,8,0,4,7,4,9,1,8,0,8,8,2,4
%N A154909 Decimal expansion of log_4 (18).
%e A154909 2.0849625007211561814537389439478165087598144076924810604557...
%K A154909 nonn,cons,new
%O A154909 1,1
%A A154909 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154905
%S A154905 4,1,6,9,9,2,5,0,0,1,4,4,2,3,1,2,3,6,2,9,0,7,4,7,7,8,8,7,8,9,5,6,3,3,0,
%T A154905 1,7,5,1,9,6,2,8,8,1,5,3,8,4,9,6,2,1,2,0,9,1,1,5,0,5,3,0,9,0,8,2,1,9,6,
%U A154905 4,5,5,5,8,8,7,1,7,1,2,5,0,4,4,5,6,0,9,4,9,8,3,6,1,7,6,4,8
%N A154905 Decimal expansion of log_2 (18).
%e A154905 4.1699250014423123629074778878956330175196288153849621209115...
%K A154905 nonn,cons,new
%O A154905 1,1
%A A154905 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154904
%S A154904 8,9,1,4,9,3,1,8,9,0,0,8,0,7,4,4,5,7,3,7,6,0,3,8,8,8,3,3,8,1,9,8,1,4,2,
%T A154904 0,1,7,9,5,8,1,4,6,3,3,8,6,0,8,3,0,2,5,2,5,8,9,9,5,0,6,9,5,9,6,1,1,1,5,
%U A154904 0,6,3,8,0,7,2,7,8,8,2,5,7,9,4,4,2,6,7,1,3,7,6,9,9,5,3,5,1
%N A154904 Decimal expansion of log_24 (17).
%e A154904 .89149318900807445737603888338198142017958146338608302525899...
%K A154904 nonn,cons,new
%O A154904 0,1
%A A154904 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154903
%S A154903 9,0,3,5,9,3,8,6,7,1,6,8,6,0,5,8,6,4,5,6,3,8,2,4,8,7,3,7,5,6,5,8,1,8,4,
%T A154903 3,8,4,0,0,7,0,1,3,6,2,6,1,8,1,9,1,8,8,7,6,0,1,5,5,8,0,0,2,7,6,9,6,7,7,
%U A154903 2,3,3,6,0,6,7,2,0,2,2,0,0,2,5,8,8,1,9,7,4,1,5,4,1,6,4,5,9
%N A154903 Decimal expansion of log_23 (17).
%e A154903 .90359386716860586456382487375658184384007013626181918876015...
%K A154903 nonn,cons,new
%O A154903 0,1
%A A154903 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154902
%S A154902 9,1,6,5,8,8,2,9,8,8,6,9,2,1,2,5,7,4,2,3,8,0,3,7,1,4,4,0,6,7,2,7,5,4,1,
%T A154902 0,2,3,1,5,4,4,9,2,3,4,6,3,9,9,2,3,5,2,9,6,2,8,2,1,2,2,5,3,0,8,4,9,3,8,
%U A154902 0,5,9,7,6,8,1,6,0,4,2,5,2,2,9,2,5,9,5,3,3,1,1,6,9,7,4,0,3
%N A154902 Decimal expansion of log_22 (17).
%e A154902 .91658829886921257423803714406727541023154492346399235296282...
%K A154902 nonn,cons,new
%O A154902 0,1
%A A154902 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154901
%S A154901 9,3,0,5,9,3,6,8,1,6,0,7,0,1,8,8,8,4,5,1,1,1,3,4,7,7,6,7,8,6,6,5,0,2,4,
%T A154901 9,3,1,8,7,9,3,0,0,0,7,8,4,0,7,5,3,6,5,5,9,8,5,2,6,0,2,3,7,6,4,8,3,1,2,
%U A154901 9,7,4,5,0,1,8,8,5,8,9,4,2,5,6,7,6,9,3,8,8,2,8,0,9,4,3,5,9
%N A154901 Decimal expansion of log_21 (17).
%e A154901 .93059368160701888451113477678665024931879300078407536559852...
%K A154901 nonn,cons,new
%O A154901 0,1
%A A154901 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154900
%S A154900 9,4,5,7,4,9,8,4,8,5,6,5,4,1,5,9,0,6,2,7,7,0,0,5,1,4,9,2,0,7,4,1,2,7,7,
%T A154900 5,4,4,8,9,6,7,2,6,9,7,7,5,2,3,9,3,1,8,2,6,2,4,2,2,8,0,2,1,1,8,7,0,6,5,
%U A154900 7,2,6,2,8,9,4,4,3,1,0,3,0,3,8,1,0,4,4,1,8,5,0,5,1,7,2,7,2
%N A154900 Decimal expansion of log_20 (17).
%e A154900 .94574984856541590627700514920741277544896726977523931826242...
%K A154900 nonn,cons,new
%O A154900 0,1
%A A154900 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154899
%S A154899 9,6,2,2,2,5,1,8,5,8,8,5,2,5,4,1,2,8,6,3,6,6,8,0,0,9,1,7,0,1,6,3,2,7,7,
%T A154899 7,4,2,0,7,5,1,1,1,2,3,5,6,8,3,0,1,4,9,7,8,0,6,2,2,3,5,0,4,6,9,0,7,7,9,
%U A154899 1,0,5,7,5,0,6,4,7,9,5,8,9,5,7,6,0,3,6,3,4,1,3,0,7,0,9,0,7
%N A154899 Decimal expansion of log_19 (17).
%e A154899 .96222518588525412863668009170163277742075111235683014978062...
%K A154899 nonn,cons,new
%O A154899 0,1
%A A154899 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154898
%S A154898 9,8,0,2,2,4,5,4,5,9,6,5,8,2,6,5,8,6,1,3,3,3,6,8,1,0,5,0,4,8,7,6,3,6,1,
%T A154898 1,5,4,2,1,7,5,7,3,7,1,1,0,3,8,0,8,9,2,7,0,7,2,2,2,6,9,1,3,4,5,6,3,7,5,
%U A154898 7,5,6,9,9,0,9,9,6,2,2,3,0,9,2,0,4,5,9,9,8,3,2,6,5,5,3,6,8
%N A154898 Decimal expansion of log_18 (17).
%e A154898 .98022454596582658613336810504876361154217573711038089270722...
%K A154898 nonn,cons,new
%O A154898 0,1
%A A154898 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154897
%S A154897 1,0,2,1,8,6,5,7,1,0,3,1,2,5,8,4,8,5,2,0,6,3,5,1,6,5,0,2,7,0,2,6,0,1,0,
%T A154897 8,8,5,0,2,8,1,6,8,2,0,5,8,6,2,0,5,1,7,2,0,3,1,6,5,2,2,6,6,0,9,6,6,7,4,
%U A154897 1,2,7,2,6,1,8,4,5,5,1,7,0,7,4,3,3,5,7,8,7,9,6,0,9,2,1,0,6
%N A154897 Decimal expansion of log_16 (17).
%e A154897 1.0218657103125848520635165027026010885028168205862051720316...
%K A154897 nonn,cons,new
%O A154897 1,3
%A A154897 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154892
%S A154892 1,0,4,6,2,1,8,9,1,5,3,2,9,9,5,3,2,8,5,4,0,7,1,3,1,1,1,2,1,4,5,8,9,2,1,
%T A154892 8,3,6,8,9,3,8,5,7,2,5,5,9,5,0,3,8,7,6,5,3,8,2,9,8,3,1,9,1,7,8,3,4,6,7,
%U A154892 0,6,9,5,7,4,1,0,6,9,1,7,9,8,9,8,5,6,3,3,4,9,3,1,8,1,5,4,2
%N A154892 Decimal expansion of log_15 (17).
%e A154892 1.0462189153299532854071311121458921836893857255950387653829...
%K A154892 nonn,cons,new
%O A154892 1,3
%A A154892 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154889
%S A154889 1,0,7,3,5,7,0,2,1,4,7,3,6,2,0,7,7,0,9,4,6,8,1,4,9,0,8,7,4,5,0,0,0,4,8,
%T A154889 7,0,6,9,0,3,4,4,5,6,7,3,9,7,4,5,8,4,8,0,5,8,5,6,7,4,3,6,2,7,6,6,7,6,5,
%U A154889 2,8,9,8,5,4,3,9,0,4,2,8,6,5,0,0,9,2,0,4,1,0,0,3,9,1,2,3,3
%N A154889 Decimal expansion of log_14 (17).
%e A154889 1.0735702147362077094681490874500048706903445673974584805856...
%K A154889 nonn,cons,new
%O A154889 1,3
%A A154889 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154885
%S A154885 1,1,0,4,5,8,8,4,1,4,5,0,9,7,4,0,3,3,7,4,3,2,4,0,5,8,4,9,2,7,1,5,9,5,4,
%T A154885 4,6,0,4,2,0,3,1,7,6,8,3,6,3,7,2,1,7,3,6,3,3,0,6,5,9,3,2,1,2,6,6,3,6,5,
%U A154885 2,2,7,3,9,2,6,3,0,4,0,8,6,0,3,4,3,3,4,9,5,8,7,1,7,1,0,6,2
%N A154885 Decimal expansion of log_13 (17).
%e A154885 1.1045884145097403374324058492715954460420317683637217363306...
%K A154885 nonn,cons,new
%O A154885 1,4
%A A154885 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154884
%S A154884 1,1,4,0,1,6,8,9,2,5,1,7,7,9,0,6,1,9,5,6,6,0,4,9,9,4,8,6,1,5,6,2,1,4,9,
%T A154884 1,0,9,7,6,5,2,7,5,4,7,5,9,7,2,8,8,9,7,7,5,5,6,9,6,0,5,4,7,5,8,6,6,4,9,
%U A154884 5,2,5,1,2,7,2,5,9,8,3,3,0,2,2,3,6,5,2,5,7,5,7,1,6,1,8,7,4
%N A154884 Decimal expansion of log_12 (17).
%e A154884 1.1401689251779061956604994861562149109765275475972889775569...
%K A154884 nonn,cons,new
%O A154884 1,3
%A A154884 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154861
%S A154861 1,1,8,1,5,4,1,7,3,6,2,8,6,8,4,9,7,9,5,9,2,3,1,5,9,4,3,4,6,2,7,2,7,0,9,
%T A154861 2,4,6,5,4,5,6,2,9,0,5,9,2,0,8,3,6,5,9,3,6,7,6,7,9,4,6,6,0,0,1,4,4,2,0,
%U A154861 3,8,1,2,9,5,2,6,7,1,7,6,6,7,1,6,3,6,1,8,5,3,9,7,1,8,8,8,4
%N A154861 Decimal expansion of log_11 (17).
%e A154861 1.1815417362868497959231594346272709246545629059208365936767...
%K A154861 nonn,cons,new
%O A154861 1,3
%A A154861 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154860
%S A154860 1,2,3,0,4,4,8,9,2,1,3,7,8,2,7,3,9,2,8,5,4,0,1,6,9,8,9,4,3,2,8,3,3,7,0,
%T A154860 3,0,0,0,7,5,6,7,3,7,8,4,2,5,0,4,6,3,9,7,3,8,0,3,6,8,4,8,2,3,4,4,6,9,4,
%U A154860 0,6,2,2,5,7,1,1,8,1,8,5,7,9,5,6,8,4,6,7,0,0,9,8,4,6,5,1,3
%N A154860 Decimal expansion of log_10 (17).
%e A154860 1.2304489213782739285401698943283370300075673784250463973803...
%K A154860 nonn,cons,new
%O A154860 1,2
%A A154860 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154859
%S A154859 1,2,8,9,4,5,0,9,6,1,5,8,1,2,8,2,9,4,6,7,5,8,1,8,7,1,2,2,3,2,0,0,8,8,8,
%T A154859 2,2,2,4,0,8,7,7,1,4,7,3,6,9,7,2,3,3,9,4,7,4,6,8,8,7,3,0,4,4,7,0,4,8,6,
%U A154859 8,4,3,5,2,6,1,9,0,7,1,2,8,1,5,0,6,9,8,7,9,9,9,5,8,1,8,9,2
%N A154859 Decimal expansion of log_9 (17).
%e A154859 1.2894509615812829467581871223200888222408771473697233947468...
%K A154859 nonn,cons,new
%O A154859 1,2
%A A154859 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154858
%S A154858 1,3,6,2,4,8,7,6,1,3,7,5,0,1,1,3,1,3,6,0,8,4,6,8,8,6,7,0,2,7,0,1,3,4,7,
%T A154858 8,4,6,7,0,4,2,2,4,2,7,4,4,8,2,7,3,5,6,2,7,0,8,8,6,9,6,8,8,1,2,8,8,9,8,
%U A154858 8,3,6,3,4,9,1,2,7,3,5,6,0,9,9,1,1,4,3,8,3,9,4,7,8,9,4,7,5
%N A154858 Decimal expansion of log_8 (17).
%e A154858 1.3624876137501131360846886702701347846704224274482735627088...
%K A154858 nonn,cons,new
%O A154858 1,2
%A A154858 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154857
%S A154857 1,4,5,5,9,8,3,6,4,1,0,9,0,3,4,7,5,9,5,9,4,2,1,0,9,3,5,8,7,9,4,1,9,4,6,
%T A154857 7,0,6,0,4,7,3,7,1,2,7,5,8,3,1,6,4,4,7,1,8,5,1,7,7,8,5,5,3,6,6,5,4,6,5,
%U A154857 7,6,0,2,3,2,0,4,8,0,6,2,0,4,9,8,9,5,3,8,7,2,2,0,3,7,2,0,1
%N A154857 Decimal expansion of log_7 (17).
%e A154857 1.4559836410903475959421093587941946706047371275831644718517...
%K A154857 nonn,cons,new
%O A154857 1,2
%A A154857 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154856
%S A154856 1,5,8,1,2,4,6,4,7,4,6,0,4,5,6,9,2,1,0,8,4,5,8,2,3,9,8,7,0,2,4,3,2,2,8,
%T A154856 1,2,4,1,3,1,8,4,8,9,2,7,0,6,0,2,0,9,8,1,3,0,6,8,0,5,5,3,3,4,7,0,4,0,0,
%U A154856 0,5,6,6,2,7,7,6,4,3,9,2,5,8,6,4,6,9,9,4,7,8,7,3,7,5,4,8,6
%N A154856 Decimal expansion of log_6 (17).
%e A154856 1.5812464746045692108458239870243228124131848927060209813068...
%K A154856 nonn,cons,new
%O A154856 1,2
%A A154856 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154850
%S A154850 1,7,6,0,3,7,4,4,2,7,7,2,2,5,8,7,9,6,0,0,9,8,6,8,1,8,6,1,2,4,8,0,5,1,7,
%T A154850 1,9,9,8,6,3,8,0,8,2,5,4,3,8,4,7,1,0,5,5,9,4,6,0,8,9,6,4,5,7,4,8,8,6,2,
%U A154850 3,7,6,8,8,5,4,0,9,9,5,2,8,0,5,8,5,0,3,4,9,4,6,0,6,8,4,9,6
%N A154850 Decimal expansion of log_5 (17).
%e A154850 1.7603744277225879600986818612480517199863808254384710559460...
%K A154850 nonn,cons,new
%O A154850 1,2
%A A154850 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154849
%S A154849 2,0,4,3,7,3,1,4,2,0,6,2,5,1,6,9,7,0,4,1,2,7,0,3,3,0,0,5,4,0,5,2,0,2,1,
%T A154849 7,7,0,0,5,6,3,3,6,4,1,1,7,2,4,1,0,3,4,4,0,6,3,3,0,4,5,3,2,1,9,3,3,4,8,
%U A154849 2,5,4,5,2,3,6,9,1,0,3,4,1,4,8,6,7,1,5,7,5,9,2,1,8,4,2,1,3
%N A154849 Decimal expansion of log_4 (17).
%e A154849 2.0437314206251697041270330054052021770056336411724103440633...
%K A154849 nonn,cons,new
%O A154849 1,1
%A A154849 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154848
%S A154848 2,5,7,8,9,0,1,9,2,3,1,6,2,5,6,5,8,9,3,5,1,6,3,7,4,2,4,4,6,4,0,1,7,7,6,
%T A154848 4,4,4,8,1,7,5,4,2,9,4,7,3,9,4,4,6,7,8,9,4,9,3,7,7,4,6,0,8,9,4,0,9,7,3,
%U A154848 6,8,7,0,5,2,3,8,1,4,2,5,6,3,0,1,3,9,7,5,9,9,9,1,6,3,7,8,5
%N A154848 Decimal expansion of log_3 (17).
%e A154848 2.5789019231625658935163742446401776444817542947394467894937...
%K A154848 nonn,cons,new
%O A154848 1,1
%A A154848 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154847
%S A154847 4,0,8,7,4,6,2,8,4,1,2,5,0,3,3,9,4,0,8,2,5,4,0,6,6,0,1,0,8,1,0,4,0,4,3,
%T A154847 5,4,0,1,1,2,6,7,2,8,2,3,4,4,8,2,0,6,8,8,1,2,6,6,0,9,0,6,4,3,8,6,6,9,6,
%U A154847 5,0,9,0,4,7,3,8,2,0,6,8,2,9,7,3,4,3,1,5,1,8,4,3,6,8,4,2,7
%N A154847 Decimal expansion of log_2 (17).
%e A154847 4.0874628412503394082540660108104043540112672823448206881266...
%K A154847 nonn,cons,new
%O A154847 1,1
%A A154847 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154846
%S A154846 8,7,2,4,1,7,1,6,7,9,4,2,1,2,6,2,3,6,9,1,7,3,5,1,2,2,5,7,7,3,5,5,3,5,5,
%T A154846 4,5,1,0,6,4,1,7,0,1,9,9,7,9,9,9,0,7,0,4,5,8,9,5,2,6,2,5,8,5,6,7,3,6,9,
%U A154846 5,2,6,0,0,3,9,6,9,4,0,3,9,1,9,6,7,0,8,5,6,7,5,2,8,8,8,5,6
%N A154846 Decimal expansion of log_24 (16).
%e A154846 .87241716794212623691735122577355355451064170199799907045895...
%K A154846 nonn,cons,new
%O A154846 0,1
%A A154846 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154845
%S A154845 8,8,4,2,5,8,9,1,7,8,3,0,0,1,4,9,8,4,5,9,9,1,8,4,2,1,6,3,8,1,7,3,4,0,5,
%T A154845 9,3,8,6,9,5,6,4,1,4,7,0,6,2,2,6,6,1,6,1,1,2,2,3,6,9,3,8,6,5,8,2,3,1,2,
%U A154845 9,1,0,4,0,8,8,9,7,1,7,3,5,3,2,7,0,0,0,2,2,6,7,3,9,3,1,7,0
%N A154845 Decimal expansion of log_23 (16).
%e A154845 .88425891783001498459918421638173405938695641470622661611223...
%K A154845 nonn,cons,new
%O A154845 0,1
%A A154845 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154842
%S A154842 8,9,6,9,7,5,2,9,6,8,7,0,3,0,1,7,5,7,9,1,0,2,4,9,3,5,3,6,1,3,9,2,1,8,8,
%T A154842 3,5,9,1,6,5,1,5,2,9,7,6,8,8,8,8,0,3,8,9,0,3,0,4,6,8,4,4,2,6,0,4,5,8,1,
%U A154842 2,0,0,2,5,6,0,5,6,9,5,6,7,0,3,1,7,9,0,7,7,2,2,8,1,5,4,6,2
%N A154842 Decimal expansion of log_22 (16).
%e A154842 .89697529687030175791024935361392188359165152976888803890304...
%K A154842 nonn,cons,new
%O A154842 0,1
%A A154842 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154839
%S A154839 9,1,0,6,8,0,9,9,4,7,8,7,8,1,1,9,9,1,9,2,8,3,0,3,8,8,8,4,0,3,5,6,3,9,8,
%T A154839 2,5,6,4,2,6,2,3,6,4,9,6,5,2,9,3,1,8,4,6,6,8,2,9,9,8,2,6,8,6,2,4,3,4,7,
%U A154839 3,7,0,2,7,4,1,9,0,7,0,3,3,1,5,3,7,9,2,6,1,0,6,9,3,6,3,5,5
%N A154839 Decimal expansion of log_21 (16).
%e A154839 .91068099478781199192830388840356398256426236496529318466829...
%K A154839 nonn,cons,new
%O A154839 0,1
%A A154839 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154838
%S A154838 9,2,5,5,1,2,8,5,2,6,3,9,0,3,6,6,9,7,0,5,4,7,9,0,8,0,4,3,9,0,5,6,1,9,8,
%T A154838 3,5,6,3,8,6,2,0,2,9,4,9,4,2,6,3,4,4,7,3,5,8,4,7,1,1,7,6,4,5,4,0,9,8,2,
%U A154838 1,6,1,2,0,6,3,3,5,3,8,8,5,5,8,6,2,3,3,6,1,7,9,0,1,5,7,0,3
%N A154838 Decimal expansion of log_20 (16).
%e A154838 .92551285263903669705479080439056198356386202949426344735847...
%K A154838 nonn,cons,new
%O A154838 0,1
%A A154838 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154837
%S A154837 9,4,1,6,3,5,6,5,3,4,6,6,5,5,2,9,4,5,7,8,7,8,6,1,8,4,0,1,4,7,3,6,7,4,1,
%T A154837 5,3,4,1,6,2,7,1,0,6,5,1,1,2,6,4,1,8,9,1,5,2,5,2,9,4,7,4,0,1,1,4,2,9,2,
%U A154837 0,8,5,2,8,2,1,7,9,2,7,0,0,9,7,6,0,1,8,3,4,9,9,1,3,4,5,4,6
%N A154837 Decimal expansion of log_19 (16).
%e A154837 .94163565346655294578786184014736741534162710651126418915252...
%K A154837 nonn,cons,new
%O A154837 0,1
%A A154837 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154830
%S A154830 9,5,9,2,4,9,8,6,6,2,7,2,5,2,5,7,7,8,9,4,2,7,3,6,6,5,9,6,4,2,0,9,2,2,4,
%T A154830 7,0,7,2,7,1,1,7,2,0,0,7,6,2,8,2,2,6,3,9,1,4,5,7,9,6,0,2,8,5,9,6,5,1,6,
%U A154830 2,2,9,7,2,7,5,8,1,7,9,4,0,2,6,2,2,5,6,5,9,2,0,5,6,4,4,9,7
%N A154830 Decimal expansion of log_18 (16).
%e A154830 .95924986627252577894273665964209224707271172007628226391457...
%K A154830 nonn,cons,new
%O A154830 0,1
%A A154830 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154827
%S A154827 9,7,8,6,0,2,1,6,8,4,7,2,9,0,4,1,2,1,5,5,9,0,4,5,9,6,4,9,2,7,9,1,1,2,2,
%T A154827 9,5,7,7,0,4,3,8,6,2,4,3,3,4,5,4,7,9,1,1,4,5,4,0,1,5,7,0,1,0,8,7,8,9,2,
%U A154827 4,4,6,2,8,2,1,0,7,4,3,7,9,7,1,0,6,0,7,5,2,1,9,2,0,1,2,3,0
%N A154827 Decimal expansion of log_17 (16).
%e A154827 .97860216847290412155904596492791122957704386243345479114540...
%K A154827 nonn,cons,new
%O A154827 0,1
%A A154827 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154826
%S A154826 1,0,2,3,8,3,2,0,9,9,2,3,9,2,6,1,9,5,7,5,5,0,7,1,0,7,1,5,4,5,9,2,0,9,0,
%T A154826 8,1,6,1,9,7,6,7,5,1,9,0,3,5,6,0,4,5,6,9,0,7,4,0,6,1,7,2,3,7,1,8,4,7,6,
%U A154826 8,7,9,0,8,8,6,8,9,9,7,8,0,5,8,9,1,0,3,3,5,4,1,1,8,1,1,1,7
%N A154826 Decimal expansion of log_15 (16).
%e A154826 1.0238320992392619575507107154592090816197675190356045690740...
%K A154826 nonn,cons,new
%O A154826 1,3
%A A154826 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154814
%S A154814 1,0,5,0,5,9,8,1,4,0,1,4,8,7,7,4,1,9,1,9,1,5,6,2,7,4,7,4,2,6,0,3,2,2,8,
%T A154814 8,2,4,0,2,6,4,6,3,7,8,8,2,7,6,7,9,2,3,9,5,6,8,1,7,0,2,6,4,4,3,0,7,8,4,
%U A154814 1,9,9,9,9,0,0,7,0,1,8,5,1,5,0,0,6,3,4,3,6,0,7,2,6,3,3,6,5
%N A154814 Decimal expansion of log_14 (16).
%e A154814 1.0505981401487741919156274742603228824026463788276792395681...
%K A154814 nonn,cons,new
%O A154814 1,3
%A A154814 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154803
%S A154803 1,0,8,0,9,5,2,6,1,7,7,0,9,2,7,8,9,6,5,1,7,6,4,3,2,0,1,3,8,0,2,5,6,9,1,
%T A154803 7,7,5,9,4,5,7,6,8,0,9,2,5,4,7,2,4,5,9,7,6,1,1,1,2,9,9,2,2,6,9,4,7,0,2,
%U A154803 7,7,4,9,3,7,8,1,2,4,8,1,2,1,2,3,3,1,5,9,7,5,0,0,5,0,8,6,9
%N A154803 Decimal expansion of log_13 (16).
%e A154803 1.0809526177092789651764320138025691775945768092547245976111...
%K A154803 nonn,cons,new
%O A154803 1,3
%A A154803 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154802
%S A154802 1,1,1,5,7,7,1,7,8,2,6,0,4,5,1,9,3,7,2,7,6,4,1,7,6,3,2,4,1,5,1,5,4,2,4,
%T A154802 1,2,4,1,9,1,7,7,3,5,0,3,8,5,8,9,2,2,7,1,8,9,0,7,8,4,0,1,3,6,3,3,1,0,6,
%U A154802 0,2,0,9,6,1,8,7,0,2,3,6,3,2,2,7,8,8,8,6,9,4,0,1,4,5,2,4,6
%N A154802 Decimal expansion of log_12 (16).
%e A154802 1.1157717826045193727641763241515424124191773503858922718907...
%K A154802 nonn,cons,new
%O A154802 1,4
%A A154802 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154801
%S A154801 1,1,5,6,2,5,9,3,0,5,2,7,1,5,5,1,4,3,7,0,6,4,8,4,4,0,3,0,8,0,1,0,5,4,2,
%T A154801 6,4,7,6,5,1,7,8,4,6,3,9,4,2,7,8,4,0,1,4,5,0,5,3,6,6,2,7,1,1,9,4,1,2,6,
%U A154801 3,3,4,2,2,7,6,6,3,0,8,7,7,3,1,9,0,8,3,6,6,1,5,6,7,9,1,2,6
%N A154801 Decimal expansion of log_11 (16).
%e A154801 1.1562593052715514370648440308010542647651784639427840145053...
%K A154801 nonn,cons,new
%O A154801 1,3
%A A154801 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154794
%S A154794 1,2,0,4,1,1,9,9,8,2,6,5,5,9,2,4,7,8,0,8,5,4,9,5,5,5,7,8,8,9,7,9,7,2,1,
%T A154794 0,7,0,7,2,7,5,9,5,2,5,8,4,8,4,3,4,1,6,5,2,4,1,7,0,9,8,4,4,5,0,8,4,3,2,
%U A154794 7,5,7,0,9,7,6,9,8,0,3,7,9,4,7,7,0,9,0,0,8,4,7,2,7,4,4,6,8
%N A154794 Decimal expansion of log_10 (16).
%e A154794 1.2041199826559247808549555788979721070727595258484341652417...
%K A154794 nonn,cons,new
%O A154794 1,2
%A A154794 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154793
%S A154793 1,4,2,4,8,2,8,7,4,8,4,3,2,0,8,8,7,0,6,0,5,6,7,0,8,3,1,2,0,0,5,1,6,2,1,
%T A154793 1,7,1,9,1,0,2,8,6,5,1,0,9,1,2,5,4,8,0,0,1,5,8,3,0,5,8,3,1,1,6,3,4,7,0,
%U A154793 3,2,1,4,3,7,0,3,7,3,7,8,6,5,5,4,9,6,2,6,2,1,9,9,0,9,1,4,4
%N A154793 Decimal expansion of log_7 (16).
%e A154793 1.4248287484320887060567083120051621171910286510912548001583...
%K A154793 nonn,cons,new
%O A154793 1,2
%A A154793 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154776
%S A154776 1,5,4,7,4,1,1,2,2,8,9,3,8,1,6,6,3,4,7,4,8,0,9,8,4,5,5,3,8,7,1,2,8,3,5,
%T A154776 0,5,8,6,0,5,6,7,4,3,7,8,2,8,4,1,3,7,1,3,5,5,7,9,7,9,7,1,5,3,0,6,5,6,8,
%U A154776 0,7,4,1,6,2,8,9,1,2,1,5,3,2,6,6,0,9,2,0,1,1,7,9,2,6,4,0,1
%N A154776 Decimal expansion of log_6 (16).
%e A154776 1.5474112289381663474809845538712835058605674378284137135579...
%K A154776 nonn,cons,new
%O A154776 1,2
%A A154776 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154759
%S A154759 1,7,2,2,7,0,6,2,3,2,2,9,3,5,7,2,2,0,2,6,8,0,4,2,6,2,7,5,0,5,5,8,6,2,5,
%T A154759 2,8,2,7,9,1,6,7,7,2,8,3,1,9,0,4,1,7,9,7,2,8,7,9,0,4,1,5,1,8,4,2,6,4,8,
%U A154759 3,3,0,1,5,1,5,4,2,0,2,4,3,3,4,7,9,2,3,9,7,7,8,1,0,6,7,9,0
%N A154759 Decimal expansion of log_5 (16).
%e A154759 1.7227062322935722026804262750558625282791677283190417972879...
%K A154759 nonn,cons,new
%O A154759 1,2
%A A154759 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154751
%S A154751 2,5,2,3,7,1,9,0,1,4,2,8,5,8,2,9,7,4,8,3,9,8,1,0,8,4,5,7,3,7,1,0,4,3,4,
%T A154751 1,7,1,9,8,3,4,2,5,6,0,5,2,7,5,2,1,7,1,1,4,8,2,6,1,9,7,7,5,3,5,4,7,4,0,
%U A154751 8,0,5,5,2,3,6,5,9,2,2,0,2,4,4,6,9,0,7,5,4,1,9,7,8,0,6,9,8
%N A154751 Decimal expansion of log_3 (16).
%e A154751 2.5237190142858297483981084573710434171983425605275217114826...
%K A154751 nonn,cons,new
%O A154751 1,1
%A A154751 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154735
%S A154735 8,5,2,1,0,9,6,0,7,2,2,0,1,2,7,6,2,7,8,2,7,0,8,5,9,9,9,8,7,7,4,2,2,4,6,
%T A154735 2,1,0,8,0,4,1,1,9,9,7,7,9,6,4,9,9,8,3,4,6,4,8,1,7,5,5,9,3,2,8,3,3,8,7,
%U A154735 4,2,7,3,9,5,0,7,8,3,2,9,6,5,2,7,0,2,2,5,0,2,0,5,7,3,9,6,8
%N A154735 Decimal expansion of log_24 (15).
%e A154735 .85210960722012762782708599987742246210804119977964998346481...
%K A154735 nonn,cons,new
%O A154735 0,1
%A A154735 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154719
%S A154719 8,6,3,6,7,5,7,1,2,5,3,8,2,6,2,8,2,2,0,6,4,8,0,6,6,8,9,1,8,4,9,5,8,5,5,
%T A154719 4,1,6,2,9,4,2,9,0,8,9,3,0,5,0,5,7,6,3,2,1,5,8,0,2,0,7,2,0,8,0,1,9,2,6,
%U A154719 2,9,6,3,7,7,9,4,9,2,1,7,7,9,1,3,3,2,7,3,1,3,8,6,4,6,1,5,0
%N A154719 Decimal expansion of log_23 (15).
%e A154719 .86367571253826282206480668918495855416294290893050576321580...
%K A154719 nonn,cons,new
%O A154719 0,1
%A A154719 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154718
%S A154718 8,7,6,0,9,6,0,8,7,9,5,8,9,3,5,2,4,0,3,2,0,7,6,1,6,8,4,7,4,1,4,6,6,3,2,
%T A154718 3,5,4,3,8,9,0,0,2,7,1,1,1,0,6,1,5,1,4,5,0,3,0,1,1,6,1,8,6,3,0,7,2,1,6,
%U A154718 4,0,1,1,0,1,5,9,1,5,8,5,2,3,8,3,9,6,6,3,9,4,2,2,7,6,8,2,2
%N A154718 Decimal expansion of log_22 (15).
%e A154718 .87609608795893524032076168474146632354389002711106151450301...
%K A154718 nonn,cons,new
%O A154718 0,1
%A A154718 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154707
%S A154707 8,8,9,4,8,2,7,5,3,5,3,3,9,7,8,2,3,7,8,8,1,1,3,9,0,4,9,5,6,3,4,2,5,1,7,
%T A154707 4,1,0,3,3,5,1,6,1,1,0,8,5,4,5,8,0,3,4,1,1,8,7,6,3,7,9,8,1,3,1,9,0,8,2,
%U A154707 3,3,2,8,3,3,9,8,5,0,4,5,8,7,3,7,3,4,8,7,7,6,8,4,5,7,2,4,9
%N A154707 Decimal expansion of log_21 (15).
%e A154707 .88948275353397823788113904956342517410335161108545803411876...
%K A154707 nonn,cons,new
%O A154707 0,1
%A A154707 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154705
%S A154705 9,0,3,9,6,9,3,6,5,0,2,2,5,6,6,2,8,0,3,8,5,4,1,1,7,4,0,4,6,4,0,5,1,6,6,
%T A154705 1,8,1,3,8,3,7,4,1,6,1,8,5,2,0,0,3,4,4,6,0,9,7,5,1,9,8,9,0,4,7,8,9,7,5,
%U A154705 8,8,8,7,1,2,5,2,3,3,9,9,5,0,8,7,4,7,6,9,6,9,4,8,9,8,5,6,3
%N A154705 Decimal expansion of log_20 (15).
%e A154705 .90396936502256628038541174046405166181383741618520034460975...
%K A154705 nonn,cons,new
%O A154705 0,1
%A A154705 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154697
%S A154697 9,1,9,7,1,6,8,6,9,7,5,4,5,3,9,3,9,8,4,9,3,6,7,6,9,3,8,9,8,3,8,6,0,4,9,
%T A154697 0,4,3,4,0,5,4,0,0,0,8,4,5,1,9,3,4,1,5,8,8,6,2,8,4,7,2,2,7,8,3,4,8,8,5,
%U A154697 8,6,5,4,1,0,1,7,1,7,8,6,3,9,0,9,4,3,5,1,5,0,5,7,6,7,8,6,9
%N A154697 Decimal expansion of log_19 (15).
%e A154697 .91971686975453939849367693898386049043405400084519341588628...
%K A154697 nonn,cons,new
%O A154697 0,1
%A A154697 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154688
%S A154688 9,3,6,9,2,1,0,7,0,3,4,4,7,1,4,9,9,7,6,3,1,2,2,0,9,8,7,6,5,4,5,8,8,0,7,
%T A154688 1,4,6,3,7,4,0,0,1,9,9,9,8,9,9,2,3,1,1,2,0,4,4,6,9,7,7,7,9,0,9,2,8,9,9,
%U A154688 6,5,4,2,7,9,7,7,2,9,9,1,2,2,2,1,2,6,9,7,4,4,9,9,7,2,2,5,1
%N A154688 Decimal expansion of log_18 (15).
%e A154688 .93692107034471499763122098765458807146374001999899231120446...
%K A154688 nonn,cons,new
%O A154688 0,1
%A A154688 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154683
%S A154683 9,5,5,8,2,2,9,0,2,2,1,2,2,2,3,0,4,4,3,0,2,0,5,9,8,5,9,2,2,9,0,3,9,1,7,
%T A154683 1,7,2,8,1,7,5,6,9,3,8,2,0,3,1,7,4,5,3,2,6,9,2,9,0,1,7,8,8,4,9,0,1,2,5,
%U A154683 9,2,5,1,6,0,6,6,1,8,5,6,6,6,5,5,2,7,5,3,9,9,6,5,6,9,0,8,0
%N A154683 Decimal expansion of log_17 (15).
%e A154683 .95582290221222304430205985922903917172817569382031745326929...
%K A154683 nonn,cons,new
%O A154683 0,1
%A A154683 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154678
%S A154678 9,7,6,7,2,2,6,4,8,9,0,2,1,2,9,6,3,2,3,3,1,0,1,4,5,9,3,3,5,9,3,0,1,6,7,
%T A154678 1,1,5,6,1,6,1,4,5,0,1,7,9,2,6,5,4,1,8,1,2,7,6,2,7,2,6,2,5,8,9,2,5,8,2,
%U A154678 5,1,1,0,0,7,4,5,9,4,4,5,9,3,1,0,5,0,5,4,5,6,9,3,6,4,5,9,9
%N A154678 Decimal expansion of log_16 (15).
%e A154678 .97672264890212963233101459335930167115616145017926541812762...
%K A154678 nonn,cons,new
%O A154678 0,1
%A A154678 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154584
%S A154584 1,0,2,6,1,4,2,9,9,8,3,7,7,7,6,1,5,5,6,5,8,1,9,5,3,2,6,2,3,9,0,4,2,1,9,
%T A154584 1,1,4,9,3,7,2,4,9,3,1,0,4,9,3,9,0,7,6,2,0,1,5,9,3,9,0,7,1,3,0,2,9,9,5,
%U A154584 2,5,9,5,8,4,1,9,5,4,0,8,7,9,3,0,5,1,9,9,0,4,9,6,0,4,1,3,2
%N A154584 Decimal expansion of log_14 (15).
%e A154584 1.0261429983777615565819532623904219114937249310493907620159...
%K A154584 nonn,cons,new
%O A154584 1,3
%A A154584 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154583
%S A154583 1,0,5,5,7,9,0,9,0,4,1,0,6,6,9,8,0,3,2,6,1,9,1,4,4,0,7,0,7,4,4,8,8,2,9,
%T A154583 9,4,9,9,2,9,9,7,0,5,3,4,0,3,2,2,8,4,9,3,3,1,7,4,0,6,1,6,7,8,5,5,9,1,8,
%U A154583 5,9,0,8,3,8,5,5,6,9,2,7,5,1,6,8,0,8,9,5,1,0,0,3,0,4,7,3,8
%N A154583 Decimal expansion of log_13 (15).
%e A154583 1.0557909041066980326191440707448829949929970534032284933174...
%K A154583 nonn,cons,new
%O A154583 1,3
%A A154583 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154582
%S A154582 1,0,8,9,7,9,9,5,7,1,0,7,5,7,3,7,2,8,6,5,3,9,8,6,1,1,8,5,0,5,3,4,3,6,1,
%T A154582 9,4,6,8,7,1,5,2,8,4,9,7,4,4,5,6,2,3,5,5,6,1,3,2,7,3,0,3,9,0,3,7,6,5,2,
%U A154582 9,7,0,0,8,1,2,7,1,5,9,7,9,6,7,5,2,8,0,6,5,9,8,3,7,7,3,4,6
%N A154582 Decimal expansion of log_12 (15).
%e A154582 1.0897995710757372865398611850534361946871528497445623556132...
%K A154582 nonn,cons,new
%O A154582 1,3
%A A154582 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154581
%S A154581 1,1,2,9,3,4,4,6,5,1,4,6,2,5,6,5,8,6,0,6,2,2,1,1,8,8,7,1,2,1,1,7,4,9,4,
%T A154581 4,2,4,0,9,6,0,5,0,8,8,0,3,7,8,2,5,1,9,8,2,5,9,2,2,9,0,9,2,1,0,0,8,4,5,
%U A154581 6,6,8,2,7,6,0,0,0,2,9,5,6,6,4,3,8,3,1,6,3,1,1,3,0,0,1,2,9
%N A154581 Decimal expansion of log_11 (15).
%e A154581 1.1293446514625658606221188712117494424096050880378251982592...
%K A154581 nonn,cons,new
%O A154581 1,3
%A A154581 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154580
%S A154580 1,1,7,6,0,9,1,2,5,9,0,5,5,6,8,1,2,4,2,0,8,1,2,8,9,0,0,8,5,3,0,6,2,2,2,
%T A154580 8,2,4,3,1,9,3,8,9,8,2,7,2,8,5,8,7,3,2,3,5,1,9,4,3,8,1,7,9,1,7,8,1,2,0,
%U A154580 9,6,3,5,0,9,2,3,6,6,1,3,5,5,6,0,4,1,1,0,3,5,2,9,4,3,0,1,2
%N A154580 Decimal expansion of log_10 (15).
%e A154580 1.1760912590556812420812890085306222824319389827285873235194...
%K A154580 nonn,cons,new
%O A154580 1,3
%A A154580 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154578
%S A154578 1,2,3,2,4,8,6,7,6,0,3,5,8,9,6,3,5,8,3,5,9,8,5,2,0,2,0,3,8,3,9,3,2,0,1,
%T A154578 9,8,1,5,3,9,6,6,1,8,3,3,3,3,0,2,4,8,4,4,5,2,6,4,4,5,1,9,7,3,9,7,7,4,6,
%U A154578 1,3,8,0,9,5,5,1,2,9,1,1,8,2,7,7,9,6,5,5,6,8,7,9,7,6,4,7,4
%N A154578 Decimal expansion of log_9 (15).
%e A154578 1.2324867603589635835985202038393201981539661833330248445264...
%K A154578 nonn,cons,new
%O A154578 1,2
%A A154578 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154574
%S A154574 1,3,0,2,2,9,6,8,6,5,2,0,2,8,3,9,5,0,9,7,7,4,6,8,6,1,2,4,4,7,9,0,6,8,8,
%T A154574 9,4,8,7,4,8,8,1,9,3,3,5,7,2,3,5,3,8,9,0,8,3,6,8,3,6,3,5,0,1,1,9,0,1,1,
%U A154574 0,0,1,4,6,7,6,6,1,2,5,9,4,5,7,4,7,3,4,0,6,0,9,2,4,8,6,1,3
%N A154574 Decimal expansion of log_8 (15).
%e A154574 1.3022968652028395097746861244790688948748819335723538908368...
%K A154574 nonn,cons,new
%O A154574 1,2
%A A154574 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154572
%S A154572 1,3,9,1,6,6,2,5,0,9,4,0,0,4,9,5,7,6,4,1,0,8,3,0,1,6,5,0,8,2,0,4,7,7,1,
%T A154572 5,5,0,1,0,9,1,5,2,7,1,3,5,6,3,7,3,6,1,8,3,6,2,1,7,3,7,1,4,9,7,2,7,9,6,
%U A154572 6,1,0,3,8,9,6,1,0,2,5,6,3,1,9,9,0,5,6,4,0,8,3,6,8,6,9,7,5
%N A154572 Decimal expansion of log_7 (15).
%e A154572 1.3916625094004957641083016508204771550109152713563736183621...
%K A154572 nonn,cons,new
%O A154572 1,2
%A A154572 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154567
%S A154567 1,5,1,1,3,9,1,5,9,4,4,6,9,3,8,5,5,8,6,2,0,2,9,8,6,8,1,9,6,1,8,6,4,7,7,
%T A154567 9,5,7,8,5,4,4,9,4,9,4,3,6,7,5,4,4,3,7,1,0,9,1,2,0,4,0,6,0,4,1,6,7,0,9,
%U A154567 1,5,6,5,3,5,4,1,6,8,2,6,4,8,3,0,2,8,3,9,6,4,7,1,3,5,3,4,7
%N A154567 Decimal expansion of log_6 (15).
%e A154567 1.5113915944693855862029868196186477957854494943675443710912...
%K A154567 nonn,cons,new
%O A154567 1,2
%A A154567 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154564
%S A154564 1,6,8,2,6,0,6,1,9,4,4,8,5,9,8,5,2,9,5,1,3,4,5,6,6,3,5,9,2,7,1,0,5,2,2,
%T A154564 5,3,0,2,4,6,6,9,3,9,9,8,7,3,1,6,7,2,0,9,6,6,0,0,5,6,6,9,1,4,9,3,7,4,6,
%U A154564 1,6,2,9,2,6,9,1,3,2,7,7,3,3,6,9,5,4,2,2,0,9,2,2,3,2,0,2,4
%N A154564 Decimal expansion of log_5 (15).
%e A154564 1.6826061944859852951345663592710522530246693998731672096600...
%K A154564 nonn,cons,new
%O A154564 1,2
%A A154564 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154543
%S A154543 1,9,5,3,4,4,5,2,9,7,8,0,4,2,5,9,2,6,4,6,6,2,0,2,9,1,8,6,7,1,8,6,0,3,3,
%T A154543 4,2,3,1,2,3,2,2,9,0,0,3,5,8,5,3,0,8,3,6,2,5,5,2,5,4,5,2,5,1,7,8,5,1,6,
%U A154543 5,0,2,2,0,1,4,9,1,8,8,9,1,8,6,2,1,0,1,0,9,1,3,8,7,2,9,1,9
%N A154543 Decimal expansion of log_4 (15).
%e A154543 1.9534452978042592646620291867186033423123229003585308362552...
%K A154543 nonn,cons,new
%O A154543 1,2
%A A154543 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154542
%S A154542 2,4,6,4,9,7,3,5,2,0,7,1,7,9,2,7,1,6,7,1,9,7,0,4,0,4,0,7,6,7,8,6,4,0,3,
%T A154542 9,6,3,0,7,9,3,2,3,6,6,6,6,6,0,4,9,6,8,9,0,5,2,8,9,0,3,9,4,7,9,5,4,9,2,
%U A154542 2,7,6,1,9,1,0,2,5,8,2,3,6,5,5,5,9,3,1,1,3,7,5,9,5,2,9,4,9
%N A154542 Decimal expansion of log_3 (15).
%e A154542 2.4649735207179271671970404076786403963079323666660496890528...
%K A154542 nonn,cons,new
%O A154542 1,1
%A A154542 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154540
%S A154540 3,9,0,6,8,9,0,5,9,5,6,0,8,5,1,8,5,2,9,3,2,4,0,5,8,3,7,3,4,3,7,2,0,6,6,
%T A154540 8,4,6,2,4,6,4,5,8,0,0,7,1,7,0,6,1,6,7,2,5,1,0,5,0,9,0,5,0,3,5,7,0,3,3,
%U A154540 0,0,4,4,0,2,9,8,3,7,7,8,3,7,2,4,2,0,2,1,8,2,7,7,4,5,8,3,9
%N A154540 Decimal expansion of log_2 (15).
%e A154540 3.9068905956085185293240583734372066846246458007170616725105...
%K A154540 nonn,cons,new
%O A154540 1,1
%A A154540 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154538
%S A154538 8,3,0,4,0,0,4,4,9,6,1,3,0,0,2,4,3,7,8,8,7,2,4,3,0,3,1,5,6,6,8,1,8,9,5,
%T A154538 9,8,3,4,3,0,1,8,2,1,3,1,3,1,1,9,1,8,5,1,6,2,2,3,6,5,4,7,0,7,4,9,5,3,4,
%U A154538 6,0,0,7,9,7,1,5,2,2,0,2,5,0,1,7,8,9,9,3,7,6,0,7,7,7,1,0,3
%N A154538 Decimal expansion of log_24 (14).
%e A154538 .83040044961300243788724303156681895983430182131311918516223...
%K A154538 nonn,cons,new
%O A154538 0,1
%A A154538 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154527
%S A154527 8,4,1,6,7,1,8,8,5,7,9,3,3,5,9,5,1,4,1,6,4,1,6,4,4,8,1,1,4,4,9,1,3,0,6,
%T A154527 6,6,0,6,6,9,2,9,5,6,9,2,8,4,7,3,1,9,0,5,6,7,4,7,1,2,7,3,5,5,5,2,9,3,1,
%U A154527 3,1,7,8,2,1,7,1,8,1,5,6,9,0,5,5,5,4,8,6,8,3,4,5,6,2,8,0,7
%N A154527 Decimal expansion of log_23 (14).
%e A154527 .84167188579335951416416448114491306660669295692847319056747...
%K A154527 nonn,cons,new
%O A154527 0,1
%A A154527 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154509
%S A154509 8,5,3,7,7,5,8,2,7,8,7,5,8,0,6,0,1,3,7,4,4,6,3,7,3,7,4,4,6,1,4,5,5,0,2,
%T A154509 1,3,2,7,6,0,0,4,7,8,2,0,7,6,9,9,3,7,1,7,4,6,5,8,2,8,7,2,5,3,6,6,3,3,0,
%U A154509 6,8,8,6,9,7,8,8,2,5,2,8,5,1,5,8,5,2,9,9,6,4,6,0,4,0,1,6,6
%N A154509 Decimal expansion of log_22 (14).
%e A154509 .85377582787580601374463737446145502132760047820769937174658...
%K A154509 nonn,cons,new
%O A154509 0,1
%A A154509 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154499
%S A154499 8,6,6,8,2,1,4,4,1,9,8,2,4,2,2,8,2,4,7,3,6,9,9,2,1,7,5,5,9,6,5,8,5,7,3,
%T A154499 5,5,7,6,6,7,9,1,1,1,4,9,2,5,6,5,6,4,8,5,0,7,4,8,6,8,1,9,6,5,4,1,3,8,7,
%U A154499 3,6,0,7,5,5,7,8,7,8,8,6,8,2,4,9,1,3,9,2,6,5,9,6,4,0,8,3,7
%N A154499 Decimal expansion of log_21 (14).
%e A154499 .86682144198242282473699217559658573557667911149256564850748...
%K A154499 nonn,cons,new
%O A154499 0,1
%A A154499 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154492
%S A154492 8,8,0,9,3,8,9,7,8,7,3,0,7,0,2,5,9,9,9,1,8,1,3,0,8,1,4,6,5,5,2,4,3,8,0,
%T A154492 5,5,9,9,2,2,4,0,4,9,0,1,1,2,4,4,6,1,5,0,5,9,0,4,2,9,5,3,6,8,6,9,6,8,5,
%U A154492 9,7,9,6,9,6,8,8,1,5,1,7,8,6,3,7,0,2,8,4,7,8,9,8,1,0,5,3,0
%N A154492 Decimal expansion of log_20 (14).
%e A154492 .88093897873070259991813081465524380559922404901124461505904...
%K A154492 nonn,cons,new
%O A154492 0,1
%A A154492 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154491
%S A154491 8,9,6,2,8,5,2,8,5,0,0,2,7,0,2,2,0,0,4,6,8,1,2,2,8,1,2,1,4,8,7,8,6,7,4,
%T A154491 2,4,1,6,7,4,9,9,8,6,1,0,8,5,2,3,6,1,1,1,7,7,7,4,4,4,6,1,3,7,0,6,3,2,4,
%U A154491 9,7,3,9,9,3,5,5,4,5,1,3,3,3,3,8,0,2,2,8,6,1,1,6,6,5,2,7,1
%N A154491 Decimal expansion of log_19 (14).
%e A154491 .89628528500270220046812281214878674241674998610852361117774...
%K A154491 nonn,cons,new
%O A154491 0,1
%A A154491 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154490
%S A154490 9,1,3,0,5,1,1,7,4,9,5,8,9,4,9,8,8,7,5,4,7,4,9,2,4,1,2,9,5,4,9,5,6,9,1,
%T A154490 2,8,1,4,0,3,6,3,3,2,7,9,1,2,2,9,0,9,0,9,8,7,4,2,7,1,5,6,8,2,5,5,3,9,4,
%U A154490 8,2,5,6,0,6,3,9,7,4,7,9,6,5,2,4,2,9,3,7,2,4,0,6,8,0,3,8,9
%N A154490 Decimal expansion of log_18 (14).
%e A154490 .91305117495894988754749241295495691281403633279122909098742...
%K A154490 nonn,cons,new
%O A154490 0,1
%A A154490 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154489
%S A154489 9,3,1,4,7,1,4,4,5,7,1,7,8,8,9,0,5,8,8,2,6,8,9,4,3,2,4,0,1,3,2,7,7,2,4,
%T A154489 6,3,3,9,4,3,1,9,0,7,1,7,9,6,6,3,9,8,0,2,5,1,6,7,5,9,7,9,4,8,0,3,6,5,9,
%U A154489 2,1,8,7,9,3,3,4,7,2,4,9,5,0,8,2,3,9,6,8,5,1,9,4,2,7,7,9,1
%N A154489 Decimal expansion of log_17 (14).
%e A154489 .93147144571788905882689432401327724633943190717966398025167...
%K A154489 nonn,cons,new
%O A154489 0,1
%A A154489 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154483
%S A154483 9,5,1,8,3,8,7,3,0,5,1,4,4,0,1,0,2,6,8,6,0,4,9,2,3,2,9,3,0,7,9,5,7,7,0,
%T A154483 2,1,6,0,2,5,6,6,5,6,4,9,1,5,3,5,1,9,5,9,1,9,3,2,2,9,3,1,0,1,7,5,8,0,2,
%U A154483 1,2,2,1,5,5,4,8,2,4,6,6,2,4,4,6,5,2,4,9,7,9,2,5,5,2,6,9,6
%N A154483 Decimal expansion of log_16 (14).
%e A154483 .95183873051440102686049232930795770216025665649153519591932...
%K A154483 nonn,cons,new
%O A154483 0,1
%A A154483 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154482
%S A154482 9,7,4,5,2,3,0,4,5,5,9,9,7,9,3,3,5,0,9,9,3,7,9,2,2,3,6,3,4,1,5,8,7,6,0,
%T A154482 8,8,8,8,3,8,2,2,3,9,7,5,4,7,1,0,1,5,5,7,3,6,7,3,3,6,1,0,3,0,0,5,9,5,4,
%U A154482 0,7,7,0,3,3,6,2,3,4,3,6,5,7,8,5,3,8,6,7,1,8,2,4,2,3,8,1,4
%N A154482 Decimal expansion of log_15 (14).
%e A154482 .97452304559979335099379223634158760888838223975471015573673...
%K A154482 nonn,cons,new
%O A154482 0,1
%A A154482 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154481
%S A154481 1,0,2,8,8,9,2,5,6,7,3,8,6,6,1,8,7,3,5,9,6,6,4,3,9,5,7,9,2,4,0,3,4,6,6,
%T A154481 0,1,6,0,7,2,9,5,9,7,7,3,9,8,7,6,2,4,3,9,4,0,3,7,6,9,9,3,2,6,3,8,7,3,0,
%U A154481 4,5,3,8,6,5,8,9,6,8,6,2,9,6,6,4,7,0,9,7,0,2,9,7,0,4,3,5,9
%N A154481 Decimal expansion of log_13 (14).
%e A154481 1.0288925673866187359664395792403466016072959773987624394037...
%K A154481 nonn,cons,new
%O A154481 1,3
%A A154481 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154480
%S A154480 1,0,6,2,0,3,4,7,9,7,0,9,8,0,7,5,9,6,2,7,4,5,9,7,6,9,5,9,6,5,2,6,9,6,2,
%T A154480 8,9,8,6,8,2,7,4,4,6,2,3,4,1,5,6,9,8,3,6,1,5,1,3,4,4,5,7,6,0,1,5,1,9,2,
%U A154480 5,7,5,9,4,3,4,9,1,8,4,1,6,2,1,5,8,6,6,1,2,9,2,9,6,0,7,8,3
%N A154480 Decimal expansion of log_12 (14).
%e A154480 1.0620347970980759627459769596526962898682744623415698361513...
%K A154480 nonn,cons,new
%O A154480 1,3
%A A154480 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154479
%S A154479 1,1,0,0,5,7,2,3,8,9,2,7,5,1,3,6,7,9,8,9,3,4,1,6,1,6,0,0,6,4,0,8,0,4,8,
%T A154479 0,4,2,8,5,2,7,5,4,1,3,9,3,8,6,1,1,8,4,1,9,9,9,6,4,1,0,7,3,8,5,5,8,9,4,
%U A154479 7,5,2,6,7,3,0,4,8,2,7,5,3,7,4,7,4,3,7,8,2,8,4,6,3,8,5,6,0
%N A154479 Decimal expansion of log_11 (14).
%e A154479 1.1005723892751367989341616006408048042852754139386118419996...
%K A154479 nonn,cons,new
%O A154479 1,5
%A A154479 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154478
%S A154478 1,1,4,6,1,2,8,0,3,5,6,7,8,2,3,8,0,2,5,9,2,5,9,5,5,1,5,3,3,1,7,1,2,9,2,
%T A154478 2,0,2,5,1,7,6,2,2,7,7,7,8,6,0,7,3,9,4,7,8,1,4,0,6,2,4,1,4,8,4,5,3,6,1,
%U A154478 6,2,9,1,7,6,5,0,3,6,7,5,5,5,3,0,3,8,7,7,9,9,6,5,6,7,4,7,4
%N A154478 Decimal expansion of log_10 (14).
%e A154478 1.1461280356782380259259551533171292202517622777860739478140...
%K A154478 nonn,cons,new
%O A154478 1,3
%A A154478 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154469
%S A154469 1,2,0,1,0,8,6,7,5,1,3,6,6,4,3,9,8,4,8,5,8,3,7,2,7,7,1,0,7,1,2,6,0,9,2,
%T A154469 8,6,1,8,3,0,2,8,4,8,7,3,6,3,0,6,1,9,5,3,6,1,9,8,2,3,7,6,0,5,5,9,2,8,5,
%U A154469 7,0,0,0,4,1,8,6,3,5,0,7,9,4,7,7,3,6,8,3,8,9,4,3,4,8,0,3,6
%N A154469 Decimal expansion of log_9 (14).
%e A154469 1.2010867513664398485837277107126092861830284873630619536198...
%K A154469 nonn,cons,new
%O A154469 1,2
%A A154469 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154468
%S A154468 1,2,6,9,1,1,8,3,0,7,3,5,2,5,3,4,7,0,2,4,8,0,6,5,6,4,3,9,0,7,7,2,7,6,9,
%T A154468 3,6,2,1,3,6,7,5,5,4,1,9,8,8,7,1,3,5,9,4,5,5,9,0,9,7,2,4,1,3,5,6,7,7,3,
%U A154468 6,1,6,2,8,7,3,9,7,6,6,2,1,6,5,9,5,3,6,6,6,3,9,0,0,7,0,2,6
%N A154468 Decimal expansion of log_8 (14).
%e A154468 1.2691183073525347024806564390772769362136755419887135945590...
%K A154468 nonn,cons,new
%O A154468 1,2
%A A154468 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154467
%S A154467 1,3,5,6,2,0,7,1,8,7,1,0,8,0,2,2,1,7,6,5,1,4,1,7,7,0,7,8,0,0,1,2,9,0,5,
%T A154467 2,9,2,9,7,7,5,7,1,6,2,7,7,2,8,1,3,7,0,0,0,3,9,5,7,6,4,5,7,7,9,0,8,6,7,
%U A154467 5,8,0,3,5,9,2,5,9,3,4,4,6,6,3,8,7,4,0,6,5,5,4,9,7,7,2,8,6
%N A154467 Decimal expansion of log_7 (14).
%e A154467 1.3562071871080221765141770780012905292977571627728137000395...
%K A154467 nonn,cons,new
%O A154467 1,2
%A A154467 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154466
%S A154466 1,4,7,2,8,8,5,9,3,9,7,3,6,2,3,3,4,2,9,8,5,6,2,8,8,1,8,9,3,9,5,6,4,2,2,
%T A154466 0,9,3,8,3,9,2,2,8,1,4,6,5,8,2,9,6,4,2,3,2,7,6,5,9,7,3,8,9,1,0,3,2,3,6,
%U A154466 6,6,4,4,1,2,8,6,8,4,5,4,8,2,1,9,9,3,9,6,1,4,8,3,9,6,0,0,3
%N A154466 Decimal expansion of log_6 (14).
%e A154466 1.4728859397362334298562881893956422093839228146582964232765...
%K A154466 nonn,cons,new
%O A154466 1,2
%A A154466 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154465
%S A154465 1,6,3,9,7,3,8,5,1,3,1,9,5,5,6,0,6,0,7,4,3,3,4,2,2,9,1,4,3,1,1,3,2,5,7,
%T A154465 0,3,1,8,6,3,4,7,8,6,1,7,9,0,5,9,3,5,7,8,0,2,8,2,1,2,2,3,8,8,1,3,5,4,0,
%U A154465 2,8,3,5,3,5,3,8,5,4,9,2,6,8,2,7,1,5,4,1,8,4,1,6,9,4,2,1,4
%N A154465 Decimal expansion of log_5 (14).
%e A154465 1.6397385131955606074334229143113257031863478617905935780282...
%K A154465 nonn,cons,new
%O A154465 1,2
%A A154465 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154464
%S A154464 1,9,0,3,6,7,7,4,6,1,0,2,8,8,0,2,0,5,3,7,2,0,9,8,4,6,5,8,6,1,5,9,1,5,4,
%T A154464 0,4,3,2,0,5,1,3,3,1,2,9,8,3,0,7,0,3,9,1,8,3,8,6,4,5,8,6,2,0,3,5,1,6,0,
%U A154464 4,2,4,4,3,1,0,9,6,4,9,3,2,4,8,9,3,0,4,9,9,5,8,5,1,0,5,3,9
%N A154464 Decimal expansion of log_4 (14).
%e A154464 1.9036774610288020537209846586159154043205133129830703918386...
%K A154464 nonn,cons,new
%O A154464 1,2
%A A154464 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154463
%S A154463 2,4,0,2,1,7,3,5,0,2,7,3,2,8,7,9,6,9,7,1,6,7,4,5,5,4,2,1,4,2,5,2,1,8,5,
%T A154463 7,2,3,6,6,0,5,6,9,7,4,7,2,6,1,2,3,9,0,7,2,3,9,6,4,7,5,2,1,1,1,8,5,7,1,
%U A154463 4,0,0,0,8,3,7,2,7,0,1,5,8,9,5,4,7,3,6,7,7,8,8,6,9,6,0,7,2
%N A154463 Decimal expansion of log_3 (14).
%e A154463 2.4021735027328796971674554214252185723660569747261239072396...
%K A154463 nonn,cons,new
%O A154463 1,1
%A A154463 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154462
%S A154462 3,8,0,7,3,5,4,9,2,2,0,5,7,6,0,4,1,0,7,4,4,1,9,6,9,3,1,7,2,3,1,8,3,0,8,
%T A154462 0,8,6,4,1,0,2,6,6,2,5,9,6,6,1,4,0,7,8,3,6,7,7,2,9,1,7,2,4,0,7,0,3,2,0,
%U A154462 8,4,8,8,6,2,1,9,2,9,8,6,4,9,7,8,6,0,9,9,9,1,7,0,2,1,0,7,8
%N A154462 Decimal expansion of log_2 (14).
%e A154462 3.8073549220576041074419693172318308086410266259661407836772...
%K A154462 nonn,cons,new
%O A154462 1,1
%A A154462 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154461
%S A154461 8,0,7,0,8,1,7,8,4,7,6,0,3,0,2,8,6,8,8,6,2,7,6,6,9,6,9,2,4,9,5,0,1,8,4,
%T A154461 9,0,1,1,5,7,0,2,0,6,9,7,2,8,8,2,0,1,8,2,0,0,7,9,4,5,7,2,2,0,7,4,8,0,1,
%U A154461 2,2,7,7,1,8,6,5,7,6,4,3,2,9,7,9,6,3,4,7,5,1,0,2,6,1,4,7,7
%N A154461 Decimal expansion of log_24 (13).
%e A154461 .80708178476030286886276696924950184901157020697288201820079...
%K A154461 nonn,cons,new
%O A154461 0,1
%A A154461 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154460
%S A154460 8,1,8,0,3,6,7,0,5,1,6,4,6,6,1,9,5,5,6,5,3,1,9,1,0,0,9,9,8,5,3,5,5,3,4,
%T A154460 3,1,6,6,3,9,6,7,5,8,6,6,6,5,0,9,5,7,4,3,1,6,3,5,9,5,0,1,1,2,1,8,1,3,0,
%U A154460 4,3,6,6,2,1,5,3,9,2,9,2,2,9,8,3,7,4,3,5,4,9,2,6,8,4,5,6,4
%N A154460 Decimal expansion of log_23 (13).
%e A154460 .81803670516466195565319100998535534316639675866650957431635...
%K A154460 nonn,cons,new
%O A154460 0,1
%A A154460 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154459
%S A154459 8,2,9,8,0,0,7,5,3,6,8,2,5,6,5,4,7,5,5,1,8,5,7,7,6,6,2,6,5,6,4,8,2,1,7,
%T A154459 8,1,1,7,6,3,8,2,9,2,9,6,1,4,0,3,5,6,0,4,5,5,6,8,6,8,1,7,3,1,0,7,3,8,8,
%U A154459 6,1,5,8,2,0,9,0,1,1,9,6,3,5,8,5,3,2,2,7,8,3,4,3,6,9,8,4,0
%N A154459 Decimal expansion of log_22 (13).
%e A154459 .82980075368256547551857766265648217811763829296140356045568...
%K A154459 nonn,cons,new
%O A154459 0,1
%A A154459 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154434
%S A154434 8,4,2,4,8,0,0,3,0,9,1,7,2,6,5,1,0,6,5,5,8,7,8,0,4,9,8,8,4,0,0,8,3,3,9,
%T A154434 8,3,3,3,4,8,6,8,6,4,7,0,7,6,2,0,9,7,5,5,4,3,8,4,5,6,3,9,7,6,3,7,8,2,7,
%U A154434 3,0,0,2,9,7,5,0,3,7,6,4,9,6,5,0,2,8,1,0,6,3,4,6,8,3,7,4,3
%N A154434 Decimal expansion of log_21 (13).
%e A154434 .84248003091726510655878049884008339833348686470762097554384...
%K A154434 nonn,cons,new
%O A154434 0,1
%A A154434 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154433
%S A154433 8,5,6,2,0,1,1,2,9,8,8,8,8,8,8,7,7,9,7,2,3,7,3,5,0,2,8,5,6,4,7,7,7,9,3,
%T A154433 8,0,4,9,9,3,9,3,6,9,2,6,1,0,2,4,9,2,4,2,5,6,8,1,3,1,2,7,8,2,6,6,9,2,8,
%U A154433 6,0,6,3,3,0,9,4,8,7,5,4,4,4,1,9,7,6,8,7,7,2,0,8,5,0,6,5,4
%N A154433 Decimal expansion of log_20 (13).
%e A154433 .85620112988888877972373502856477793804993936926102492425681...
%K A154433 nonn,cons,new
%O A154433 0,1
%A A154433 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154401
%S A154401 8,7,1,1,1,6,4,9,3,0,2,6,3,4,3,5,7,8,4,4,9,3,9,1,2,8,5,3,6,2,0,6,4,4,4,
%T A154401 3,3,9,2,0,9,0,3,2,5,7,7,7,5,2,9,4,2,7,1,7,6,0,8,5,9,7,8,1,9,7,6,0,8,6,
%U A154401 7,3,3,3,4,4,6,6,9,3,3,0,1,0,1,1,2,7,3,0,0,6,3,1,7,9,9,3,5
%N A154401 Decimal expansion of log_19 (13).
%e A154401 .87111649302634357844939128536206444339209032577752942717608...
%K A154401 nonn,cons,new
%O A154401 0,1
%A A154401 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154400
%S A154400 8,8,7,4,1,1,5,7,6,1,9,4,0,9,6,4,1,0,1,4,2,8,3,3,7,6,9,8,2,2,9,8,4,8,6,
%T A154400 9,4,5,9,8,6,0,7,9,9,3,4,2,2,3,7,8,6,3,3,1,6,5,1,7,1,1,7,6,0,4,2,9,0,4,
%U A154400 3,1,6,3,2,5,5,2,1,7,5,8,1,0,8,4,7,7,4,4,3,4,9,3,3,1,6,8,3
%N A154400 Decimal expansion of log_18 (13).
%e A154400 .88741157619409641014283376982298486945986079934223786331651...
%K A154400 nonn,cons,new
%O A154400 0,1
%A A154400 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154399
%S A154399 9,0,5,3,1,4,5,8,3,1,1,9,0,3,3,7,2,8,0,8,5,4,6,0,3,5,9,6,8,0,9,0,9,0,7,
%T A154399 9,4,9,0,9,5,4,6,7,5,7,6,3,8,5,4,4,7,1,2,0,2,0,4,0,2,5,9,7,5,4,8,4,1,5,
%U A154399 8,6,0,0,1,6,2,6,3,0,5,3,6,2,5,3,2,5,1,4,6,5,4,0,2,1,6,6,3
%N A154399 Decimal expansion of log_17 (13).
%e A154399 .90531458311903372808546035968090907949095467576385447120204...
%K A154399 nonn,cons,new
%O A154399 0,1
%A A154399 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154398
%S A154398 9,2,5,1,0,9,9,2,9,5,3,5,2,7,3,0,4,0,0,9,9,2,0,3,1,6,3,5,6,4,1,7,3,6,8,
%T A154398 3,4,0,7,1,0,9,1,0,0,4,4,7,7,5,9,3,4,2,3,8,4,6,1,5,8,8,1,4,6,0,7,1,3,7,
%U A154398 9,6,6,5,8,2,5,6,3,2,5,0,3,6,8,4,4,1,3,2,5,7,0,2,8,8,7,2,4
%N A154398 Decimal expansion of log_16 (13).
%e A154398 .92510992953527304009920316356417368340710910044775934238461...
%K A154398 nonn,cons,new
%O A154398 0,1
%A A154398 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154397
%S A154397 9,4,7,1,5,7,2,4,1,1,8,3,1,8,4,3,0,3,8,7,3,0,8,7,8,2,2,4,5,5,6,1,1,8,0,
%T A154397 1,3,1,0,6,9,3,6,9,3,2,4,1,3,1,3,0,4,5,0,2,9,1,6,0,6,5,1,6,8,0,6,2,1,8,
%U A154397 9,3,9,8,2,4,7,6,3,6,6,5,7,5,2,1,8,0,7,9,5,5,0,0,4,6,1,9,3
%N A154397 Decimal expansion of log_15 (13).
%e A154397 .94715724118318430387308782245561180131069369324131304502916...
%K A154397 nonn,cons,new
%O A154397 0,1
%A A154397 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154396
%S A154396 9,7,1,9,1,8,7,7,1,4,0,2,9,2,1,4,0,2,5,2,0,1,0,1,5,7,9,8,2,1,0,3,3,4,8,
%T A154396 3,8,3,0,6,2,3,7,6,3,7,0,7,3,7,8,4,2,8,2,5,4,3,3,5,1,2,9,3,7,4,9,1,9,2,
%U A154396 9,6,9,1,1,0,3,5,7,0,8,9,3,0,2,8,2,4,6,8,4,5,2,6,5,7,7,3,3
%N A154396 Decimal expansion of log_14 (13).
%e A154396 .97191877140292140252010157982103348383062376370737842825433...
%K A154396 nonn,cons,new
%O A154396 0,1
%A A154396 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154395
%S A154395 1,0,3,2,2,1,1,5,5,5,1,8,2,7,1,2,9,0,6,1,4,8,6,1,9,9,8,6,0,2,7,6,9,4,0,
%T A154395 2,6,8,2,4,9,0,5,6,2,2,7,8,2,3,2,8,0,6,0,1,9,8,2,4,2,5,5,5,8,7,2,6,2,8,
%U A154395 4,1,4,1,1,9,5,2,7,7,2,4,5,4,8,0,1,0,6,4,4,9,1,3,3,3,2,8,9
%N A154395 Decimal expansion of log_12 (13).
%e A154395 1.0322115551827129061486199860276940268249056227823280601982...
%K A154395 nonn,cons,new
%O A154395 1,3
%A A154395 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154394
%S A154394 1,0,6,9,6,6,6,9,6,4,4,2,4,2,6,8,7,0,9,1,3,8,6,0,1,7,7,3,9,4,7,9,5,6,4,
%T A154394 1,3,1,9,7,6,1,9,5,4,0,9,3,9,6,6,2,1,8,3,0,3,7,1,7,8,1,1,7,1,8,2,3,8,6,
%U A154394 7,1,7,9,9,0,0,0,8,0,9,7,0,9,0,5,9,8,1,3,0,2,3,3,2,5,4,1,7
%N A154394 Decimal expansion of log_11 (13).
%e A154394 1.0696669644242687091386017739479564131976195409396621830371...
%K A154394 nonn,cons,new
%O A154394 1,3
%A A154394 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154368
%S A154368 1,1,1,3,9,4,3,3,5,2,3,0,6,8,3,6,7,6,9,2,0,6,5,0,5,1,5,7,9,4,2,3,2,8,4,
%T A154368 3,0,8,2,9,7,2,9,1,8,8,3,8,7,0,6,8,2,7,1,8,0,1,1,9,0,9,7,4,9,9,7,5,5,3,
%U A154368 0,9,1,6,3,0,1,9,4,2,4,0,8,0,7,6,4,7,4,5,4,2,5,8,8,9,9,6,5
%N A154368 Decimal expansion of log_10 (13).
%e A154368 1.1139433523068367692065051579423284308297291883870682718011...
%K A154368 nonn,cons,new
%O A154368 1,4
%A A154368 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154339
%S A154339 1,1,6,7,3,5,8,7,5,9,7,3,6,3,9,6,3,4,6,6,8,9,8,0,1,2,0,3,6,2,2,2,6,4,2,
%T A154339 4,7,9,3,0,8,8,3,2,9,3,3,6,2,4,1,5,6,7,3,2,1,9,6,1,2,0,8,7,4,8,3,7,2,6,
%U A154339 5,9,4,3,7,4,1,9,7,4,5,8,6,9,5,8,7,8,6,7,6,3,8,7,1,5,0,7,1
%N A154339 Decimal expansion of log_9 (13).
%e A154339 1.1673587597363963466898012036222642479308832933624156732196...
%K A154339 nonn,cons,new
%O A154339 1,3
%A A154339 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154309
%S A154309 1,2,3,3,4,7,9,9,0,6,0,4,7,0,3,0,7,2,0,1,3,2,2,7,0,8,8,4,7,5,2,2,3,1,5,
%T A154309 7,7,8,7,6,1,4,5,4,6,7,2,6,3,6,7,9,1,2,3,1,7,9,4,8,7,8,4,1,9,4,7,6,1,8,
%U A154309 3,9,5,5,4,4,3,4,1,7,6,6,7,1,5,7,9,2,1,7,6,7,6,0,3,8,4,9,6
%N A154309 Decimal expansion of log_8 (13).
%e A154309 1.2334799060470307201322708847522315778761454672636791231794...
%K A154309 nonn,cons,new
%O A154309 1,2
%A A154309 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154294
%S A154294 1,3,1,8,1,2,3,2,2,3,0,6,1,8,4,0,8,5,9,9,7,5,8,1,0,1,7,1,1,1,5,0,9,1,4,
%T A154294 1,7,9,9,3,0,2,9,2,4,9,6,7,3,9,8,9,5,8,4,7,3,7,4,2,5,3,2,0,1,8,4,1,6,6,
%U A154294 2,8,8,3,9,5,3,6,0,7,1,9,6,3,7,7,2,5,0,6,0,2,3,9,2,6,0,9,1
%N A154294 Decimal expansion of log_7 (13).
%e A154294 1.3181232230618408599758101711150914179930292496739895847374...
%K A154294 nonn,cons,new
%O A154294 1,2
%A A154294 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154278
%S A154278 1,4,3,1,5,2,5,4,9,2,9,6,5,0,7,7,3,2,7,9,0,5,6,9,9,3,1,1,5,6,9,1,9,4,6,
%T A154278 2,9,4,5,5,1,0,3,7,4,8,2,5,1,9,5,8,2,1,1,8,1,9,6,4,0,7,5,3,9,6,5,7,8,9,
%U A154278 3,2,2,1,2,6,0,1,9,2,0,1,5,7,0,4,1,4,3,3,9,0,7,9,3,5,6,4,9
%N A154278 Decimal expansion of log_6 (13).
%e A154278 1.4315254929650773279056993115691946294551037482519582118196...
%K A154278 nonn,cons,new
%O A154278 1,2
%A A154278 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154265
%S A154265 1,5,9,3,6,9,2,6,4,1,1,6,7,0,8,2,2,8,9,7,3,5,6,8,7,2,3,4,5,3,0,1,5,2,0,
%T A154265 0,2,8,9,1,3,5,1,9,7,0,7,0,9,6,6,9,1,7,8,0,6,2,8,7,5,5,1,8,9,5,6,5,2,1,
%U A154265 5,5,6,3,3,2,3,9,4,6,6,2,2,6,5,0,1,5,3,0,0,7,0,3,1,7,6,7,6
%N A154265 Decimal expansion of log_5 (13).
%e A154265 1.5936926411670822897356872345301520028913519707096691780628...
%K A154265 nonn,cons,new
%O A154265 1,2
%A A154265 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154224
%S A154224 1,8,5,0,2,1,9,8,5,9,0,7,0,5,4,6,0,8,0,1,9,8,4,0,6,3,2,7,1,2,8,3,4,7,3,
%T A154224 6,6,8,1,4,2,1,8,2,0,0,8,9,5,5,1,8,6,8,4,7,6,9,2,3,1,7,6,2,9,2,1,4,2,7,
%U A154224 5,9,3,3,1,6,5,1,2,6,5,0,0,7,3,6,8,8,2,6,5,1,4,0,5,7,7,4,4
%N A154224 Decimal expansion of log_4 (13).
%e A154224 1.8502198590705460801984063271283473668142182008955186847692...
%K A154224 nonn,cons,new
%O A154224 1,2
%A A154224 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154217
%S A154217 2,3,3,4,7,1,7,5,1,9,4,7,2,7,9,2,6,9,3,3,7,9,6,0,2,4,0,7,2,4,4,5,2,8,4,
%T A154217 9,5,8,6,1,7,6,6,5,8,6,7,2,4,8,3,1,3,4,6,4,3,9,2,2,4,1,7,4,9,6,7,4,5,3,
%U A154217 1,8,8,7,4,8,3,9,4,9,1,7,3,9,1,7,5,7,3,5,2,7,7,4,3,0,1,4,2
%N A154217 Decimal expansion of log_3 (13).
%e A154217 2.3347175194727926933796024072445284958617665867248313464392...
%K A154217 nonn,cons,new
%O A154217 1,1
%A A154217 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154216
%S A154216 7,8,1,8,9,5,7,0,8,0,1,4,4,6,8,4,4,0,7,7,0,6,6,2,1,9,3,5,5,6,6,1,1,6,1,
%T A154216 1,3,7,2,3,3,9,5,7,4,5,0,0,5,0,0,2,3,2,3,8,5,2,6,1,8,4,3,5,3,5,8,1,5,7,
%U A154216 6,1,8,4,9,9,0,0,7,6,4,9,0,2,0,0,8,2,2,8,5,8,1,1,7,7,7,8,5
%N A154216 Decimal expansion of log_24 (12).
%e A154216 .78189570801446844077066219355661161137233957450050023238526...
%K A154216 nonn,cons,new
%O A154216 0,1
%A A154216 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154215
%S A154215 7,9,2,5,0,8,7,6,5,3,3,7,2,1,8,4,6,9,7,0,6,2,1,5,5,1,6,8,3,4,8,3,8,4,6,
%T A154215 1,5,4,9,9,7,8,0,5,9,8,6,8,2,5,1,6,5,0,0,5,0,2,4,4,1,3,8,9,6,4,2,3,4,4,
%U A154215 5,4,3,7,6,6,2,1,7,6,7,3,9,6,1,1,3,2,7,1,0,4,0,6,4,1,2,2,1
%N A154215 Decimal expansion of log_23 (12).
%e A154215 .79250876533721846970621551683483846154997805986825165005024...
%K A154215 nonn,cons,new
%O A154215 0,1
%A A154215 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154214
%S A154214 8,0,3,9,0,5,7,0,0,8,3,8,3,1,4,6,1,1,4,3,5,4,1,0,7,4,7,5,8,9,1,2,5,3,2,
%T A154214 9,3,1,6,0,0,4,1,0,6,7,1,5,6,6,0,7,5,5,7,5,7,7,3,6,6,5,0,0,2,0,8,8,7,7,
%U A154214 7,8,0,4,4,8,9,5,9,5,9,2,1,0,7,6,4,6,4,5,6,1,6,5,2,2,3,6,5
%N A154214 Decimal expansion of log_22 (12).
%e A154214 .80390570083831461143541074758912532931600410671566075575773...
%K A154214 nonn,cons,new
%O A154214 0,1
%A A154214 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154213
%S A154213 8,1,6,1,8,9,3,0,4,1,0,8,4,3,6,1,6,9,2,0,9,2,3,5,7,4,0,7,0,6,0,8,7,2,5,
%T A154213 1,3,4,6,5,1,7,6,6,2,2,3,1,4,0,4,2,3,9,9,9,3,7,3,8,0,5,0,4,9,2,6,8,7,3,
%U A154213 1,6,6,9,4,9,8,5,5,1,4,0,6,6,1,6,2,0,5,1,9,2,0,5,6,1,4,2,8
%N A154213 Decimal expansion of log_21 (12).
%e A154213 .81618930410843616920923574070608725134651766223140423999373...
%K A154213 nonn,cons,new
%O A154213 0,1
%A A154213 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154212
%S A154212 8,2,9,4,8,2,2,1,7,6,6,1,6,0,2,9,7,7,4,4,0,2,0,2,5,4,4,8,5,4,6,1,3,6,4,
%T A154212 5,3,7,7,6,9,9,4,4,5,6,7,9,4,6,3,7,9,1,9,6,8,2,2,3,1,6,5,5,0,1,9,9,5,8,
%U A154212 0,4,9,9,1,8,8,5,8,7,8,8,0,6,7,3,7,1,0,5,8,7,3,9,1,4,2,6,7
%N A154212 Decimal expansion of log_20 (12).
%e A154212 .82948221766160297744020254485461364537769944567946379196822...
%K A154212 nonn,cons,new
%O A154212 0,1
%A A154212 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154211
%S A154211 8,4,3,9,3,2,1,2,6,7,5,4,9,1,3,4,2,1,7,7,2,1,6,3,2,8,8,1,7,8,8,7,6,7,4,
%T A154211 3,8,9,6,4,3,0,3,0,1,5,0,7,7,6,8,4,5,2,5,6,5,1,3,0,9,7,8,9,5,2,5,9,4,7,
%U A154211 9,5,9,8,7,1,5,6,2,8,0,5,2,8,9,1,0,1,4,1,6,6,6,2,5,7,4,4,3
%N A154211 Decimal expansion of log_19 (12).
%e A154211 .84393212675491342177216328817887674389643030150776845256513...
%K A154211 nonn,cons,new
%O A154211 0,1
%A A154211 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154210
%S A154210 8,5,9,7,1,8,6,9,9,8,5,2,1,9,7,1,6,7,1,0,3,5,2,6,2,4,7,3,6,5,7,8,4,5,9,
%T A154210 2,6,5,2,2,6,6,8,9,5,0,2,8,6,0,5,8,4,8,9,6,7,9,6,7,3,5,1,0,7,2,3,6,9,3,
%U A154210 5,8,6,1,4,7,8,4,3,1,7,2,7,5,9,8,3,4,6,2,2,2,0,2,1,1,6,8,6
%N A154210 Decimal expansion of log_18 (12).
%e A154210 .85971869985219716710352624736578459265226689502860584896796...
%K A154210 nonn,cons,new
%O A154210 0,1
%A A154210 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154209
%S A154209 8,7,7,0,6,3,0,1,9,2,7,4,9,4,2,1,3,6,2,1,5,7,2,2,3,4,3,1,9,8,3,7,4,2,6,
%T A154209 1,6,1,9,1,9,5,5,6,0,6,6,0,6,0,3,6,3,7,9,1,9,4,5,9,0,0,0,3,4,5,2,0,3,9,
%U A154209 3,5,1,0,7,4,5,8,4,2,8,9,5,2,9,4,3,8,6,4,8,0,7,4,8,2,0,3,0
%N A154209 Decimal expansion of log_17 (12).
%e A154209 .87706301927494213621572234319837426161919556066060363791945...
%K A154209 nonn,cons,new
%O A154209 0,1
%A A154209 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154208
%S A154208 8,9,6,2,4,0,6,2,5,1,8,0,2,8,9,0,4,5,3,6,3,4,3,4,7,3,5,9,8,6,9,5,4,1,2,
%T A154208 7,1,8,9,9,5,3,6,0,1,9,2,3,1,2,0,2,6,5,1,1,3,9,3,8,1,6,3,6,3,5,2,7,4,5,
%U A154208 5,6,9,4,8,5,8,9,6,4,0,6,3,0,5,7,0,1,1,8,7,2,9,5,2,2,0,6,0
%N A154208 Decimal expansion of log_16 (12).
%e A154208 .89624062518028904536343473598695412718995360192312026511393...
%K A154208 nonn,cons,new
%O A154208 0,1
%A A154208 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154207
%S A154207 9,1,7,5,9,9,9,2,0,7,0,1,8,4,3,8,7,3,1,5,8,2,6,0,3,5,4,3,3,0,9,9,7,0,7,
%T A154207 0,3,0,9,7,5,1,5,3,7,7,8,4,0,8,2,7,1,1,9,6,3,3,7,7,8,8,8,0,4,0,4,0,9,6,
%U A154207 1,2,8,3,3,4,1,7,7,8,5,4,1,0,0,6,9,9,5,8,8,1,9,4,5,9,8,4,7
%N A154207 Decimal expansion of log_15 (12).
%e A154207 .91759992070184387315826035433099707030975153778408271196337...
%K A154207 nonn,cons,new
%O A154207 0,1
%A A154207 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154206
%S A154206 9,4,1,5,8,8,7,3,3,9,4,0,1,8,6,3,1,0,4,9,4,3,5,4,4,2,9,4,7,2,7,1,3,1,7,
%T A154206 0,1,8,8,1,2,2,1,8,3,1,3,8,2,5,5,5,3,6,5,3,0,4,9,1,3,6,9,8,7,9,4,9,1,8,
%U A154206 4,5,1,7,2,1,4,4,9,7,6,4,7,3,2,7,0,3,0,7,0,3,8,0,1,2,2,3,4
%N A154206 Decimal expansion of log_14 (12).
%e A154206 .94158873394018631049435442947271317018812218313825553653049...
%K A154206 nonn,cons,new
%O A154206 0,1
%A A154206 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154205
%S A154205 9,6,8,7,9,3,6,4,9,8,8,6,0,3,4,1,6,3,5,7,8,9,9,0,3,8,4,8,2,2,2,4,9,1,6,
%T A154205 5,7,0,3,9,1,9,3,3,3,0,1,1,0,4,6,9,1,5,8,0,5,3,8,5,5,3,0,3,3,6,6,3,3,5,
%U A154205 0,9,9,9,2,3,0,9,7,7,7,8,0,4,9,0,2,3,1,7,5,6,3,9,3,0,1,2,9
%N A154205 Decimal expansion of log_13 (12).
%e A154205 .96879364988603416357899038482224916570391933301104691580538...
%K A154205 nonn,cons,new
%O A154205 0,1
%A A154205 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154204
%S A154204 1,0,3,6,2,8,6,5,6,2,6,2,7,1,0,1,9,4,1,0,1,4,6,4,0,2,4,9,2,9,3,2,7,9,7,
%T A154204 5,1,3,0,7,2,0,8,6,1,7,5,9,6,2,0,9,3,3,5,9,1,5,0,0,2,6,0,7,8,2,4,3,6,1,
%U A154204 9,6,9,7,3,8,3,4,2,8,0,8,3,1,0,4,1,0,2,3,1,5,6,2,9,8,1,1,4
%N A154204 Decimal expansion of log_11 (12).
%e A154204 1.0362865626271019410146402492932797513072086175962093359150...
%K A154204 nonn,cons,new
%O A154204 1,3
%A A154204 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154203
%S A154203 1,0,7,9,1,8,1,2,4,6,0,4,7,6,2,4,8,2,7,7,2,2,5,0,5,6,9,2,7,0,4,1,0,1,3,
%T A154203 6,2,7,3,6,5,0,8,6,2,7,1,1,4,9,1,2,9,4,7,4,5,0,7,2,0,5,6,2,5,5,9,4,4,5,
%U A154203 5,3,1,3,3,2,5,1,0,1,4,2,0,1,6,8,2,2,8,5,9,8,8,3,9,8,8,6,4
%N A154203 Decimal expansion of log_10 (12).
%e A154203 1.0791812460476248277225056927041013627365086271149129474507...
%K A154203 nonn,cons,new
%O A154203 1,3
%A A154203 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154202
%S A154202 1,1,3,0,9,2,9,7,5,3,5,7,1,4,5,7,4,3,7,0,9,9,5,2,7,1,1,4,3,4,2,7,6,0,8,
%T A154202 5,4,2,9,9,5,8,5,6,4,0,1,3,1,8,8,0,4,2,7,8,7,0,6,5,4,9,4,3,8,3,8,6,8,5,
%U A154202 2,0,1,3,8,0,9,1,4,8,0,5,0,6,1,1,7,2,6,8,8,5,4,9,4,5,1,7,4
%N A154202 Decimal expansion of log_9 (12).
%e A154202 1.1309297535714574370995271143427608542995856401318804278706...
%K A154202 nonn,cons,new
%O A154202 1,3
%A A154202 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154201
%S A154201 1,1,9,4,9,8,7,5,0,0,2,4,0,3,8,5,3,9,3,8,1,7,9,1,2,9,8,1,3,1,5,9,3,8,8,
%T A154201 3,6,2,5,3,2,7,1,4,6,9,2,3,0,8,2,7,0,2,0,1,5,1,9,1,7,5,5,1,5,1,3,6,9,9,
%U A154201 4,0,9,2,6,4,7,8,6,1,8,7,5,0,7,4,2,6,8,2,4,9,7,2,6,9,6,0,8
%N A154201 Decimal expansion of log_8 (12).
%e A154201 1.1949875002403853938179129813159388362532714692308270201519...
%K A154201 nonn,cons,new
%O A154201 1,3
%A A154201 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154200
%S A154200 1,2,7,6,9,8,9,4,0,8,2,6,9,6,2,3,9,6,6,8,3,2,9,0,4,3,2,3,1,7,7,4,8,9,5,
%T A154200 9,4,7,3,8,7,4,2,2,3,6,7,3,2,4,1,9,9,9,5,1,2,4,5,6,2,1,7,7,8,8,9,4,8,7,
%U A154200 4,7,4,9,1,8,9,2,8,1,8,8,3,3,8,0,2,9,6,7,5,6,8,3,9,0,6,9,8
%N A154200 Decimal expansion of log_7 (12).
%e A154200 1.2769894082696239668329043231774895947387422367324199951245...
%K A154200 nonn,cons,new
%O A154200 1,2
%A A154200 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154199
%S A154199 1,3,8,6,8,5,2,8,0,7,2,3,4,5,4,1,5,8,6,8,7,0,2,4,6,1,3,8,4,6,7,8,2,0,8,
%T A154199 7,6,4,6,5,1,4,1,8,5,9,4,5,7,1,0,3,4,2,8,3,8,9,4,9,4,9,2,8,8,2,6,6,4,2,
%U A154199 0,1,8,5,4,0,7,2,2,8,0,3,8,3,1,6,5,2,3,0,0,2,9,4,8,1,6,0,0
%N A154199 Decimal expansion of log_6 (12).
%e A154199 1.3868528072345415868702461384678208764651418594571034283894...
%K A154199 nonn,cons,new
%O A154199 1,2
%A A154199 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154198
%S A154198 1,5,4,3,9,5,9,3,1,0,6,3,2,7,7,1,3,9,6,4,7,4,7,7,9,4,9,6,7,9,8,9,8,3,5,
%T A154198 1,7,1,6,4,2,5,3,2,6,4,0,3,2,6,8,8,1,0,8,3,0,4,0,0,8,7,6,7,4,1,5,0,7,0,
%U A154198 3,2,8,0,0,2,6,8,4,2,8,9,5,0,4,3,5,0,4,1,9,8,1,2,8,5,4,1,9
%N A154198 Decimal expansion of log_5 (12).
%e A154198 1.5439593106327713964747794967989835171642532640326881083040...
%K A154198 nonn,cons,new
%O A154198 1,2
%A A154198 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154197
%S A154197 1,7,9,2,4,8,1,2,5,0,3,6,0,5,7,8,0,9,0,7,2,6,8,6,9,4,7,1,9,7,3,9,0,8,2,
%T A154197 5,4,3,7,9,9,0,7,2,0,3,8,4,6,2,4,0,5,3,0,2,2,7,8,7,6,3,2,7,2,7,0,5,4,9,
%U A154197 1,1,3,8,9,7,1,7,9,2,8,1,2,6,1,1,4,0,2,3,7,4,5,9,0,4,4,1,2
%N A154197 Decimal expansion of log_4 (12).
%e A154197 1.7924812503605780907268694719739082543799072038462405302278...
%K A154197 nonn,cons,new
%O A154197 1,2
%A A154197 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154196
%S A154196 2,2,6,1,8,5,9,5,0,7,1,4,2,9,1,4,8,7,4,1,9,9,0,5,4,2,2,8,6,8,5,5,2,1,7,
%T A154196 0,8,5,9,9,1,7,1,2,8,0,2,6,3,7,6,0,8,5,5,7,4,1,3,0,9,8,8,7,6,7,7,3,7,0,
%U A154196 4,0,2,7,6,1,8,2,9,6,1,0,1,2,2,3,4,5,3,7,7,0,9,8,9,0,3,4,9
%N A154196 Decimal expansion of log_3 (12).
%e A154196 2.2618595071429148741990542286855217085991712802637608557413...
%K A154196 nonn,cons,new
%O A154196 1,1
%A A154196 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154195
%S A154195 7,5,4,5,1,6,8,8,3,8,5,5,2,4,9,1,4,1,3,8,2,4,9,4,9,1,1,3,6,5,4,8,7,8,9,
%T A154195 6,3,7,9,1,7,3,2,9,9,9,9,6,6,2,5,3,3,5,6,0,2,8,1,6,7,5,5,8,2,6,6,9,7,0,
%U A154195 3,5,3,9,3,6,0,6,6,5,6,4,4,3,8,5,1,0,0,3,3,2,8,7,6,5,1,6,8
%N A154195 Decimal expansion of log_24 (11).
%e A154195 .75451688385524914138249491136548789637917329999662533560281...
%K A154195 nonn,cons,new
%O A154195 0,1
%A A154195 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154194
%S A154194 7,6,4,7,5,8,3,1,4,8,5,0,7,8,8,3,9,2,3,0,9,7,7,1,8,7,7,8,0,8,6,2,7,7,7,
%T A154194 9,3,5,9,0,5,4,2,0,0,4,0,6,1,3,7,8,7,1,3,7,8,5,7,1,6,5,2,8,5,9,9,8,3,8,
%U A154194 2,7,7,1,3,6,7,8,4,2,6,4,3,5,8,6,4,4,9,3,7,7,3,5,4,7,3,0,3
%N A154194 Decimal expansion of log_23 (11).
%e A154194 .76475831485078839230977187780862777935905420040613787137857...
%K A154194 nonn,cons,new
%O A154194 0,1
%A A154194 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154193
%S A154193 7,7,5,7,5,6,1,7,5,7,8,2,4,2,4,5,6,0,5,2,2,4,3,7,6,6,1,5,9,6,5,1,9,5,2,
%T A154193 9,1,0,2,0,8,7,1,1,7,5,5,7,7,7,7,9,9,0,2,7,4,2,3,8,2,8,8,9,3,4,8,8,5,4,
%U A154193 6,9,9,9,3,5,9,8,5,7,6,0,8,2,4,2,0,5,2,3,0,6,9,2,9,6,1,3,4
%N A154193 Decimal expansion of log_22 (11).
%e A154193 .77575617578242456052243766159651952910208711755777799027423...
%K A154193 nonn,cons,new
%O A154193 0,1
%A A154193 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154192
%S A154192 7,8,7,6,0,9,6,5,6,9,6,5,2,5,6,1,2,6,2,9,1,8,7,8,5,7,0,7,6,7,9,0,2,2,9,
%T A154192 4,5,0,2,6,3,3,4,4,9,7,6,6,5,8,6,1,6,6,0,8,4,9,6,1,7,4,1,4,2,5,2,6,9,2,
%U A154192 7,2,9,1,0,8,5,8,3,1,4,5,8,4,7,3,0,4,7,9,5,0,1,4,9,0,1,5,8
%N A154192 Decimal expansion of log_21 (11).
%e A154192 .78760965696525612629187857076790229450263344976658616608496...
%K A154192 nonn,cons,new
%O A154192 0,1
%A A154192 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154191
%S A154191 8,0,0,4,3,7,1,0,6,4,6,8,6,7,1,2,7,3,1,0,4,4,3,3,5,7,3,6,7,1,6,7,0,7,5,
%T A154191 3,5,2,1,7,8,3,8,0,5,2,8,1,6,8,6,0,4,2,9,4,4,3,7,6,6,4,1,8,4,7,4,1,7,2,
%U A154191 3,2,3,7,8,3,9,1,4,7,9,7,0,1,8,8,7,2,1,4,3,4,9,2,8,3,9,3,4
%N A154191 Decimal expansion of log_20 (11).
%e A154191 .80043710646867127310443357367167075352178380528168604294437...
%K A154191 nonn,cons,new
%O A154191 0,1
%A A154191 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154190
%S A154190 8,1,4,3,8,1,0,3,8,2,0,9,5,9,6,5,9,6,1,0,5,8,2,4,4,0,0,8,3,2,8,7,7,6,7,
%T A154190 6,5,6,7,8,1,8,0,6,8,3,3,5,3,7,8,7,7,4,2,0,5,6,6,9,5,5,1,5,0,9,5,2,7,4,
%U A154190 3,8,1,6,9,6,1,1,5,3,4,5,0,3,7,8,1,5,2,7,9,9,5,0,1,9,9,4,3
%N A154190 Decimal expansion of log_19 (11).
%e A154190 .81438103820959659610582440083287767656781806833537877420566...
%K A154190 nonn,cons,new
%O A154190 0,1
%A A154190 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154189
%S A154189 8,2,9,6,1,4,8,2,9,3,8,9,1,9,3,6,9,8,0,4,4,9,1,7,1,0,3,7,0,8,6,0,6,8,3,
%T A154189 5,3,7,4,4,2,0,1,2,6,7,0,7,6,1,1,3,7,0,1,8,2,9,6,0,5,1,4,5,9,1,1,8,8,4,
%U A154189 5,3,4,8,9,3,1,8,8,2,3,2,5,5,4,1,7,4,2,2,8,2,0,5,6,8,0,2,5
%N A154189 Decimal expansion of log_18 (11).
%e A154189 .82961482938919369804491710370860683537442012670761137018296...
%K A154189 nonn,cons,new
%O A154189 0,1
%A A154189 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154188
%S A154188 8,4,6,3,5,1,8,2,0,9,2,0,5,4,6,9,4,2,8,2,0,6,0,1,9,2,0,4,6,1,7,0,7,8,8,
%T A154188 2,7,7,7,9,5,6,3,4,0,6,8,1,4,0,7,0,2,8,7,0,9,1,4,9,7,6,2,7,7,4,7,4,4,2,
%U A154188 6,9,8,1,9,3,7,7,0,9,4,5,9,9,5,2,0,5,1,9,8,4,4,3,4,8,8,9,7
%N A154188 Decimal expansion of log_17 (11).
%e A154188 .84635182092054694282060192046170788277795634068140702870914...
%K A154188 nonn,cons,new
%O A154188 0,1
%A A154188 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154187
%S A154187 8,6,4,8,5,7,9,0,4,6,5,9,3,2,4,3,1,4,0,4,9,8,4,0,7,6,1,6,8,1,4,4,8,2,3,
%T A154187 9,6,7,5,8,0,7,8,8,1,4,2,0,4,4,2,0,1,7,8,2,8,2,0,0,4,1,1,4,3,1,5,8,2,6,
%U A154187 5,4,9,3,0,0,0,4,5,8,8,1,7,7,3,7,2,8,2,4,8,2,1,7,2,5,1,2,2
%N A154187 Decimal expansion of log_16 (11).
%e A154187 .86485790465932431404984076168144823967580788142044201782820...
%K A154187 nonn,cons,new
%O A154187 0,1
%A A154187 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154186
%S A154186 8,8,5,4,6,9,2,8,4,0,7,1,0,2,5,4,8,7,6,4,7,3,7,9,5,2,6,7,7,0,8,1,2,3,4,
%T A154186 5,3,0,2,8,8,8,5,0,4,9,0,1,0,3,1,6,8,1,9,0,1,6,9,1,9,8,5,5,2,5,5,1,3,6,
%U A154186 6,2,7,0,8,3,8,6,0,1,2,1,2,2,0,0,9,2,8,3,0,6,2,5,7,8,4,6,2
%N A154186 Decimal expansion of log_15 (11).
%e A154186 .88546928407102548764737952677081234530288850490103168190169...
%K A154186 nonn,cons,new
%O A154186 0,1
%A A154186 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154185
%S A154185 9,0,8,6,1,8,1,0,6,1,2,8,0,5,1,9,9,3,8,8,5,0,7,2,3,3,5,7,8,5,4,0,0,0,4,
%T A154185 0,9,3,7,5,2,6,0,6,8,6,2,2,1,1,8,6,3,6,6,5,8,4,5,4,2,4,5,9,8,2,6,8,5,2,
%U A154185 5,7,1,7,8,2,0,1,0,7,0,4,8,4,0,5,5,2,4,7,1,6,3,1,7,8,1,0,9
%N A154185 Decimal expansion of log_14 (11).
%e A154185 .90861810612805199388507233578540004093752606862211863665845...
%K A154185 nonn,cons,new
%O A154185 0,1
%A A154185 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154184
%S A154184 9,3,4,8,7,0,4,1,5,9,8,8,0,5,8,6,3,0,3,6,5,3,2,8,0,8,8,6,1,3,5,5,5,7,7,
%T A154184 4,1,1,4,0,9,7,4,4,9,5,7,6,0,3,0,7,0,5,4,0,4,9,4,9,5,7,6,8,3,3,8,1,6,8,
%U A154184 7,1,3,7,8,3,9,8,8,9,5,2,5,3,2,7,5,7,2,1,8,8,4,8,2,4,7,9,3
%N A154184 Decimal expansion of log_13 (11).
%e A154184 .93487041598805863036532808861355577411409744957603070540494...
%K A154184 nonn,cons,new
%O A154184 0,1
%A A154184 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154183
%S A154183 9,6,4,9,8,4,0,4,5,9,8,1,3,4,3,7,5,0,8,5,8,1,1,3,0,0,6,2,4,7,2,5,4,9,1,
%T A154183 2,5,8,1,8,0,7,7,7,1,8,6,5,2,9,3,8,7,8,0,0,7,3,0,6,4,3,4,7,5,6,3,6,6,3,
%U A154183 0,3,6,5,5,6,3,3,3,2,7,3,9,3,7,1,2,4,5,6,7,7,4,6,9,3,8,6,4
%N A154183 Decimal expansion of log_12 (11).
%e A154183 .96498404598134375085811300624725491258180777186529387800730...
%K A154183 nonn,cons,new
%O A154183 0,1
%A A154183 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154182
%S A154182 1,0,4,1,3,9,2,6,8,5,1,5,8,2,2,5,0,4,0,7,5,0,1,9,9,9,7,1,2,4,3,0,2,4,2,
%T A154182 4,1,7,0,6,7,0,2,1,9,0,4,6,6,4,5,3,0,9,4,5,9,6,5,3,9,0,1,8,6,7,9,7,5,3,
%U A154182 0,3,2,2,3,3,2,4,9,3,4,7,5,7,1,2,9,4,7,8,6,3,8,5,7,3,1,1,7
%N A154182 Decimal expansion of log_10 (11).
%e A154182 1.0413926851582250407501999712430242417067021904664530945965...
%K A154182 nonn,cons,new
%O A154182 1,3
%A A154182 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154181
%S A154181 1,0,9,1,3,2,9,1,6,9,3,2,2,0,6,9,0,4,0,5,2,4,4,9,0,2,0,7,3,6,5,9,6,4,4,
%T A154181 6,1,7,7,1,4,8,0,7,6,2,6,0,0,4,7,2,1,8,0,1,1,8,6,4,6,5,0,5,0,8,5,9,0,4,
%U A154181 3,1,6,9,4,5,7,0,6,1,8,1,6,6,2,6,3,0,5,1,5,0,8,1,9,8,5,4,4
%N A154181 Decimal expansion of log_9 (11).
%e A154181 1.0913291693220690405244902073659644617714807626004721801186...
%K A154181 nonn,cons,new
%O A154181 1,3
%A A154181 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154180
%S A154180 1,1,5,3,1,4,3,8,7,2,8,7,9,0,9,9,0,8,5,3,9,9,7,8,7,6,8,2,2,4,1,9,3,0,9,
%T A154180 8,6,2,3,4,4,1,0,5,0,8,5,6,0,5,8,9,3,5,7,1,0,4,2,6,7,2,1,5,2,4,2,1,1,0,
%U A154180 2,0,6,5,7,3,3,3,9,4,5,0,9,0,3,1,6,3,7,6,6,4,2,8,9,6,6,8,2
%N A154180 Decimal expansion of log_8 (11).
%e A154180 1.1531438728790990853997876822419309862344105085605893571042...
%K A154180 nonn,cons,new
%O A154180 1,3
%A A154180 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154179
%S A154179 1,2,3,2,2,7,4,4,0,5,8,6,7,3,4,3,7,6,1,8,6,0,7,5,6,8,6,7,6,5,5,6,2,9,2,
%T A154179 9,9,1,5,2,8,3,9,8,9,3,2,8,6,8,1,7,5,5,5,6,2,6,3,2,3,1,3,4,7,9,6,8,2,9,
%U A154179 5,0,4,2,4,1,7,7,0,0,9,0,8,8,8,6,7,3,7,6,0,2,9,7,1,2,1,1,1
%N A154179 Decimal expansion of log_7 (11).
%e A154179 1.2322744058673437618607568676556292991528398932868175556263...
%K A154179 nonn,cons,new
%O A154179 1,2
%A A154179 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154178
%S A154178 1,3,3,8,2,9,0,8,3,3,1,0,5,7,7,2,5,3,9,9,5,8,4,1,7,6,1,0,8,7,2,9,8,3,1,
%T A154178 9,8,4,1,1,6,5,6,8,1,7,2,2,1,0,3,9,8,5,6,5,7,1,6,0,4,5,6,2,2,0,8,3,3,1,
%U A154178 6,2,0,8,7,4,8,5,7,1,3,8,4,0,9,2,3,9,4,3,5,3,9,1,0,3,5,2,2
%N A154178 Decimal expansion of log_6 (11).
%e A154178 1.3382908331057725399584176108729831984116568172210398565716...
%K A154178 nonn,cons,new
%O A154178 1,2
%A A154178 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154177
%S A154177 1,4,8,9,8,9,6,1,0,2,4,0,4,9,7,8,0,7,2,7,9,9,2,0,1,7,7,9,9,8,3,9,7,1,3,
%T A154177 0,7,6,1,3,4,8,0,4,4,4,5,5,9,6,3,3,7,5,0,5,2,7,3,5,2,6,0,6,5,1,1,2,9,8,
%U A154177 8,2,2,5,3,5,4,0,6,9,1,4,8,3,4,6,2,4,9,2,3,3,9,4,4,1,9,5,6
%N A154177 Decimal expansion of log_5 (11).
%e A154177 1.4898961024049780727992017799839713076134804445596337505273...
%K A154177 nonn,cons,new
%O A154177 1,2
%A A154177 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154176
%S A154176 1,7,2,9,7,1,5,8,0,9,3,1,8,6,4,8,6,2,8,0,9,9,6,8,1,5,2,3,3,6,2,8,9,6,4,
%T A154176 7,9,3,5,1,6,1,5,7,6,2,8,4,0,8,8,4,0,3,5,6,5,6,4,0,0,8,2,2,8,6,3,1,6,5,
%U A154176 3,0,9,8,6,0,0,0,9,1,7,6,3,5,4,7,4,5,6,4,9,6,4,3,4,5,0,2,4
%N A154176 Decimal expansion of log_4 (11).
%e A154176 1.7297158093186486280996815233628964793516157628408840356564...
%K A154176 nonn,cons,new
%O A154176 1,2
%A A154176 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154175
%S A154175 2,1,8,2,6,5,8,3,3,8,6,4,4,1,3,8,0,8,1,0,4,8,9,8,0,4,1,4,7,3,1,9,2,8,9,
%T A154175 2,3,5,4,2,9,6,1,5,2,5,2,0,0,9,4,4,3,6,0,2,3,7,2,9,3,0,1,0,1,7,1,8,0,8,
%U A154175 6,3,3,8,9,1,4,1,2,3,6,3,3,2,5,2,6,1,0,3,0,1,6,3,9,7,0,8,9
%N A154175 Decimal expansion of log_3 (11).
%e A154175 2.1826583386441380810489804147319289235429615252009443602372...
%K A154175 nonn,cons,new
%O A154175 1,1
%A A154175 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154174
%S A154174 7,2,4,5,2,6,7,7,5,1,6,2,2,5,3,8,6,4,7,4,4,4,3,7,2,2,5,6,5,0,9,7,6,0,1,
%T A154174 6,6,1,8,6,8,2,9,0,1,7,7,7,6,4,9,0,5,3,9,2,3,7,7,0,1,8,5,1,8,5,0,7,5,6,
%U A154174 9,5,3,3,9,9,0,4,7,7,3,3,5,7,2,3,7,3,1,0,6,9,5,8,6,2,8,2,5
%N A154174 Decimal expansion of log_24 (10).
%e A154174 .72452677516225386474443722565097601661868290177764905392377...
%K A154174 nonn,cons,new
%O A154174 0,1
%A A154174 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154173
%S A154173 7,3,4,3,6,1,1,3,5,5,7,3,5,5,5,5,9,0,8,0,7,9,7,9,3,3,4,6,3,6,4,2,0,6,3,
%T A154173 7,1,5,3,1,8,2,1,6,0,0,9,1,9,2,4,0,7,5,2,4,9,7,3,5,6,3,7,1,0,9,6,3,1,6,
%U A154173 4,3,5,4,1,8,4,0,4,4,2,3,9,7,9,7,2,5,0,3,7,9,8,5,4,9,8,0,6
%N A154173 Decimal expansion of log_23 (10).
%e A154173 .73436113557355559080797933463642063715318216009192407524973...
%K A154173 nonn,cons,new
%O A154173 0,1
%A A154173 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154172
%S A154172 7,4,4,9,2,1,8,5,9,7,7,3,3,4,6,9,4,7,3,1,8,0,3,7,9,5,2,3,6,2,7,8,2,4,0,
%T A154172 6,9,2,1,6,2,4,5,6,7,7,2,2,0,6,6,7,8,7,9,2,2,5,6,0,1,0,1,8,0,5,1,7,7,4,
%U A154172 5,2,0,8,4,4,6,7,4,7,1,0,6,5,8,1,3,4,4,9,1,1,7,8,6,6,0,5,3
%N A154172 Decimal expansion of log_22 (10).
%e A154172 .74492185977334694731803795236278240692162456772206678792256...
%K A154172 nonn,cons,new
%O A154172 0,1
%A A154172 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154171
%S A154171 7,5,6,3,0,4,1,9,5,5,1,6,4,0,1,0,6,2,6,1,8,1,3,1,2,2,5,1,6,0,0,1,0,9,0,
%T A154171 9,6,8,0,0,3,0,7,2,2,5,7,8,0,2,3,6,8,2,6,2,6,2,5,0,6,1,7,7,8,6,0,4,6,9,
%U A154171 6,9,3,5,8,9,7,7,2,9,3,2,6,9,8,6,4,8,8,0,4,2,8,0,9,8,0,8,7
%N A154171 Decimal expansion of log_21 (10).
%e A154171 .75630419551640106261813122516001090968003072257802368262625...
%K A154171 nonn,cons,new
%O A154171 0,1
%A A154171 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154170
%S A154170 7,6,8,6,2,1,7,8,6,8,4,0,2,4,0,8,2,5,7,3,6,3,0,2,2,9,8,9,0,2,3,5,9,5,0,
%T A154170 4,1,0,9,0,3,4,4,9,2,6,2,6,4,3,4,1,3,8,1,6,0,3,8,2,2,0,5,8,8,6,4,7,5,4,
%U A154170 4,5,9,6,9,8,4,1,6,1,5,2,8,6,0,3,4,4,1,5,9,5,5,2,4,6,0,7,4
%N A154170 Decimal expansion of log_20 (10).
%e A154170 .76862178684024082573630229890235950410903449262643413816038...
%K A154170 nonn,cons,new
%O A154170 0,1
%A A154170 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154169
%S A154169 7,8,2,0,1,1,4,8,3,0,9,9,5,4,0,6,8,6,0,6,2,4,1,0,0,3,0,9,1,5,5,0,9,3,0,
%T A154169 8,0,4,3,8,4,4,0,2,9,2,2,0,8,7,3,1,0,5,1,8,5,5,5,0,8,4,9,3,3,9,4,6,5,6,
%U A154169 9,6,9,5,0,0,2,4,3,4,3,3,6,7,5,0,4,3,4,7,4,6,3,8,6,1,3,3,6
%N A154169 Decimal expansion of log_19 (10).
%e A154169 .78201148309954068606241003091550930804384402922087310518555...
%K A154169 nonn,cons,new
%O A154169 0,1
%A A154169 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154168
%S A154168 7,9,6,6,3,9,7,7,0,1,9,6,9,1,2,1,6,4,7,3,4,7,4,7,2,3,5,0,2,0,3,7,2,6,6,
%T A154168 4,1,1,6,0,0,6,9,1,5,0,2,7,5,9,8,1,6,0,1,7,2,4,3,7,1,2,8,9,8,1,6,5,9,3,
%U A154168 2,4,0,4,2,7,6,1,6,1,6,3,9,8,1,9,6,1,5,9,6,7,0,1,8,3,9,3,8
%N A154168 Decimal expansion of log_18 (10).
%e A154168 .79663977019691216473474723502037266411600691502759816017243...
%K A154168 nonn,cons,new
%O A154168 0,1
%A A154168 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154167
%S A154167 8,1,2,7,1,1,5,0,9,2,9,1,9,5,8,9,9,9,2,5,5,6,2,1,9,8,9,7,2,6,5,9,8,3,3,
%T A154167 2,2,9,1,7,6,3,0,2,9,9,8,4,8,0,4,9,0,8,7,0,8,8,8,2,3,5,6,0,8,5,4,0,0,5,
%U A154167 9,0,8,7,9,7,6,5,8,1,4,5,6,1,4,3,8,4,4,5,6,0,3,4,8,7,9,7,2
%N A154167 Decimal expansion of log_17 (10).
%e A154167 .81271150929195899925562198972659833229176302998480490870888...
%K A154167 nonn,cons,new
%O A154167 0,1
%A A154167 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154166
%S A154166 8,3,0,4,8,2,0,2,3,7,2,1,8,4,0,5,8,6,9,6,7,5,7,9,8,5,7,3,7,2,3,4,7,5,4,
%T A154166 3,9,6,6,2,0,7,8,4,8,2,5,6,1,4,5,1,5,3,0,1,3,6,8,9,0,9,8,9,5,3,9,8,3,6,
%U A154166 9,4,1,5,2,1,5,6,3,0,3,9,6,2,5,3,4,9,3,5,8,3,9,8,4,2,5,3,8
%N A154166 Decimal expansion of log_16 (10).
%e A154166 .83048202372184058696757985737234754396620784825614515301368...
%K A154166 nonn,cons,new
%O A154166 0,1
%A A154166 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154165
%S A154165 8,5,0,2,7,4,1,5,3,7,2,7,6,0,2,5,9,5,0,0,4,7,7,2,6,8,2,2,6,3,4,0,9,7,4,
%T A154165 0,9,0,5,0,7,4,1,0,1,4,9,2,6,2,0,7,1,4,8,4,2,1,6,8,4,0,4,7,4,8,4,4,8,0,
%U A154165 4,6,4,8,3,0,9,9,6,9,8,1,3,4,1,1,2,7,9,2,7,3,9,3,9,8,5,3,6
%N A154165 Decimal expansion of log_15 (10).
%e A154165 .85027415372760259500477268226340974090507410149262071484216...
%K A154165 nonn,cons,new
%O A154165 0,1
%A A154165 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154164
%S A154164 8,7,2,5,0,2,8,6,9,5,4,9,1,5,5,8,9,0,0,2,4,3,1,9,4,3,8,6,1,2,9,5,0,9,0,
%T A154164 3,1,0,7,5,8,7,5,3,2,0,3,1,8,9,4,6,5,5,1,6,1,5,7,5,3,9,9,7,4,6,5,9,1,5,
%U A154164 6,4,4,0,4,6,0,3,0,7,1,1,8,2,3,2,9,2,6,0,5,1,2,5,0,4,3,3,3
%N A154164 Decimal expansion of log_14 (10).
%e A154164 .87250286954915589002431943861295090310758753203189465516157...
%K A154164 nonn,cons,new
%O A154164 0,1
%A A154164 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154163
%S A154163 8,9,7,7,1,1,7,1,7,5,0,2,6,2,3,0,9,2,9,2,2,4,7,7,6,9,6,2,7,4,5,6,0,7,1,
%T A154163 2,4,8,5,0,1,0,3,2,7,3,3,3,2,2,5,0,2,5,7,2,0,3,6,8,0,7,9,5,4,0,3,1,2,1,
%U A154163 6,2,0,4,9,6,0,6,5,1,0,6,2,1,1,5,5,3,3,1,5,6,4,4,9,8,7,7,5
%N A154163 Decimal expansion of log_13 (10).
%e A154163 .89771171750262309292247769627456071248501032733322502572036...
%K A154163 nonn,cons,new
%O A154163 0,1
%A A154163 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154162
%S A154162 9,2,6,6,2,8,4,0,8,0,2,9,1,2,6,8,1,6,1,1,2,9,9,3,4,2,8,1,6,7,0,9,3,0,0,
%T A154162 4,0,0,1,5,3,5,8,6,2,5,3,3,9,8,1,5,5,9,5,3,1,3,6,1,0,4,9,2,6,2,4,8,2,4,
%U A154162 8,5,8,0,2,6,7,4,2,7,5,2,0,9,6,1,9,7,1,8,0,3,4,8,6,2,8,1,0
%N A154162 Decimal expansion of log_12 (10).
%e A154162 .92662840802912681611299342816709300400153586253398155953136...
%K A154162 nonn,cons,new
%O A154162 0,1
%A A154162 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154161
%S A154161 9,6,0,2,5,2,5,6,7,7,8,9,1,2,7,4,9,7,4,0,6,1,1,1,6,4,5,0,1,9,2,6,0,3,8,
%T A154161 9,6,7,6,2,8,0,3,1,8,3,9,8,7,0,3,8,7,3,2,2,3,2,5,1,1,8,7,6,7,2,0,7,8,4,
%U A154161 4,9,2,0,8,4,0,4,8,0,3,1,5,2,9,0,4,2,0,6,1,6,7,6,1,3,5,9,6
%N A154161 Decimal expansion of log_11 (10).
%e A154161 .96025256778912749740611164501926038967628031839870387322325...
%K A154161 nonn,cons,new
%O A154161 0,1
%A A154161 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154160
%S A154160 1,0,4,7,9,5,1,6,3,7,1,4,4,6,9,2,3,0,2,1,4,8,2,8,3,7,6,1,0,1,0,7,0,0,6,
%T A154160 2,5,3,0,3,7,5,9,0,0,3,3,9,8,9,6,5,0,5,8,4,6,1,7,7,2,6,6,9,3,1,7,0,8,8,
%U A154160 7,3,8,7,8,5,9,7,0,3,1,4,3,5,8,3,8,2,9,0,1,1,5,4,4,9,0,6,1
%N A154160 Decimal expansion of log_9 (10).
%e A154160 1.0479516371446923021482837610107006253037590033989650584617...
%K A154160 nonn,cons,new
%O A154160 1,3
%A A154160 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154159
%S A154159 1,1,0,7,3,0,9,3,6,4,9,6,2,4,5,4,1,1,5,9,5,6,7,7,3,1,4,3,1,6,3,1,3,0,0,
%T A154159 5,8,6,2,1,6,1,0,4,6,4,3,4,1,5,2,6,8,7,0,6,8,4,9,1,8,7,9,8,6,0,5,3,1,1,
%U A154159 5,9,2,2,0,2,8,7,5,0,7,1,9,5,0,0,4,6,5,8,1,1,1,9,7,9,0,0,5
%N A154159 Decimal expansion of log_8 (10).
%e A154159 1.1073093649624541159567731431631300586216104643415268706849...
%K A154159 nonn,cons,new
%O A154159 1,4
%A A154159 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154158
%S A154158 1,1,8,3,2,9,4,6,6,2,4,5,4,9,3,8,3,2,6,8,1,7,9,2,8,5,6,1,6,4,6,8,5,9,1,
%T A154158 4,8,1,6,5,4,4,4,5,2,2,9,4,2,3,9,4,7,2,3,3,5,6,3,4,0,9,1,0,4,5,5,9,1,1,
%U A154158 8,7,6,5,4,8,4,6,0,1,0,1,9,7,3,4,9,8,1,6,1,8,0,2,2,8,1,3,5
%N A154158 Decimal expansion of log_7 (10).
%e A154158 1.1832946624549383268179285616468591481654445229423947233563...
%K A154158 nonn,cons,new
%O A154158 1,3
%A A154158 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154157
%S A154157 1,2,8,5,0,9,7,2,0,8,9,3,8,4,6,8,7,5,9,9,4,3,4,7,9,0,9,6,5,5,4,2,8,9,5,
%T A154157 4,8,7,1,5,7,3,3,2,1,3,2,8,1,7,5,1,2,2,7,8,7,0,1,9,3,9,1,8,0,6,9,9,9,3,
%U A154157 1,9,3,6,1,6,8,6,2,4,3,4,1,4,6,3,3,2,9,9,7,0,6,0,9,8,5,4,8
%N A154157 Decimal expansion of log_6 (10).
%e A154157 1.2850972089384687599434790965542895487157332132817512278701...
%K A154157 nonn,cons,new
%O A154157 1,2
%A A154157 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154156
%S A154156 1,4,3,0,6,7,6,5,5,8,0,7,3,3,9,3,0,5,0,6,7,0,1,0,6,5,6,8,7,6,3,9,6,5,6,
%T A154156 3,2,0,6,9,7,9,1,9,3,2,0,7,9,7,6,0,4,4,9,3,2,1,9,7,6,0,3,7,9,6,0,6,6,2,
%U A154156 0,8,2,5,3,7,8,8,5,5,0,6,0,8,3,6,9,8,0,9,9,4,4,5,2,6,6,9,7
%N A154156 Decimal expansion of log_5 (10).
%e A154156 1.4306765580733930506701065687639656320697919320797604493219...
%K A154156 nonn,cons,new
%O A154156 1,2
%A A154156 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154155
%S A154155 1,6,6,0,9,6,4,0,4,7,4,4,3,6,8,1,1,7,3,9,3,5,1,5,9,7,1,4,7,4,4,6,9,5,0,
%T A154155 8,7,9,3,2,4,1,5,6,9,6,5,1,2,2,9,0,3,0,6,0,2,7,3,7,8,1,9,7,9,0,7,9,6,7,
%U A154155 3,8,8,3,0,4,3,1,2,6,0,7,9,2,5,0,6,9,8,7,1,6,7,9,6,8,5,0,7
%N A154155 Decimal expansion of log_4 (10).
%e A154155 1.6609640474436811739351597147446950879324156965122903060273...
%K A154155 nonn,cons,new
%O A154155 1,2
%A A154155 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154116
%S A154116 6,9,1,3,7,4,2,4,8,0,8,6,8,1,0,6,4,4,6,2,3,9,7,3,1,6,1,3,3,9,6,6,9,6,6,
%T A154116 8,2,3,4,0,3,7,4,4,7,0,0,3,0,0,1,3,9,4,3,1,1,5,7,1,0,6,1,2,1,4,8,9,4,5,
%U A154116 7,1,0,9,9,4,0,4,5,8,9,4,1,2,0,4,9,3,7,1,4,8,7,0,6,6,7,1,4
%N A154116 Decimal expansion of log_24 (9).
%e A154116 .69137424808681064462397316133966966823403744700300139431157...
%K A154116 nonn,cons,new
%O A154116 0,1
%A A154116 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154102
%S A154102 7,0,0,7,5,8,6,1,2,8,4,4,4,2,1,9,5,4,8,1,3,2,4,6,8,1,7,2,8,7,9,4,2,8,6,
%T A154102 3,7,1,2,9,9,9,7,0,5,0,3,0,2,7,6,6,8,3,9,8,8,2,5,1,3,3,9,2,7,0,2,3,7,6,
%U A154102 1,7,7,1,2,3,5,3,8,1,7,4,3,8,9,5,6,5,3,9,8,1,3,8,8,9,2,7,3
%N A154102 Decimal expansion of log_23 (9).
%e A154102 .70075861284442195481324681728794286371299970503027668398825...
%K A154102 nonn,cons,new
%O A154102 0,1
%A A154102 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154098
%S A154098 7,1,0,8,3,6,1,0,4,8,0,6,3,2,7,4,6,4,9,6,0,5,7,2,1,4,1,5,6,4,3,2,8,7,7,
%T A154098 5,0,4,0,3,5,6,6,8,3,6,6,2,4,3,3,4,7,2,6,1,2,4,2,6,4,5,5,7,8,1,3,1,7,4,
%U A154098 3,6,0,6,4,1,8,6,2,2,2,7,5,1,2,1,1,3,8,3,5,1,0,2,2,9,2,6,8
%N A154098 Decimal expansion of log_22 (9).
%e A154098 .71083610480632746496057214156432877504035668366243347261242...
%K A154098 nonn,cons,new
%O A154098 0,1
%A A154098 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154020
%S A154020 7,2,1,6,9,7,6,1,3,4,2,9,0,6,0,3,4,6,4,9,0,1,6,7,5,9,3,0,0,8,6,1,0,5,2,
%T A154020 0,1,2,8,7,7,2,9,5,9,4,9,7,5,1,5,2,9,5,3,1,9,1,7,6,2,7,4,1,2,2,9,3,9,8,
%U A154020 9,6,3,6,2,5,5,1,9,5,7,8,0,0,7,8,6,1,7,7,7,3,4,1,8,6,5,0,2
%N A154020 Decimal expansion of log_21 (9).
%e A154020 .72169761342906034649016759300861052012877295949751529531917...
%K A154020 nonn,cons,new
%O A154020 0,1
%A A154020 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154019
%S A154019 7,3,3,4,5,1,5,8,2,6,8,4,1,6,9,2,5,7,8,2,5,6,1,4,2,8,5,3,1,8,6,6,5,3,0,
%T A154019 7,1,9,1,5,3,6,8,6,1,8,6,4,6,6,4,1,3,6,5,7,7,9,7,5,1,5,4,5,4,9,8,9,3,3,
%U A154019 9,3,8,6,3,1,3,8,2,1,8,7,5,7,6,1,1,8,7,5,5,6,8,8,1,2,8,3,0
%N A154019 Decimal expansion of log_20 (9).
%e A154019 .73345158268416925782561428531866530719153686186466413657797...
%K A154019 nonn,cons,new
%O A154019 0,1
%A A154019 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154018
%S A154018 7,4,6,2,2,8,6,0,0,0,4,3,2,7,3,8,9,7,7,5,6,4,6,4,7,3,6,2,1,0,3,8,6,0,7,
%T A154018 2,4,5,1,2,3,3,4,9,6,5,0,4,2,7,2,7,1,5,9,7,7,7,3,2,4,8,3,8,9,3,7,6,0,3,
%U A154018 8,3,4,4,6,0,9,4,6,3,4,0,4,8,0,6,0,0,9,9,8,3,3,3,8,0,3,4,0
%N A154018 Decimal expansion of log_19 (9).
%e A154018 .74622860004327389775646473621038607245123349650427271597773...
%K A154018 nonn,cons,new
%O A154018 0,1
%A A154018 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154017
%S A154017 7,6,0,1,8,7,5,3,3,4,3,1,8,6,8,5,5,5,2,6,4,3,1,5,8,3,5,0,8,9,4,7,6,9,3,
%T A154017 8,2,3,1,8,2,2,0,6,9,9,8,0,9,2,9,4,3,4,0,2,1,3,5,5,0,9,9,2,8,5,0,8,7,0,
%U A154017 9,4,2,5,6,8,1,0,4,5,5,1,4,9,3,4,4,3,5,8,5,1,9,8,5,8,8,7,5
%N A154017 Decimal expansion of log_18 (9).
%e A154017 .76018753343186855526431583508947693823182206998092943402135...
%K A154017 nonn,cons,new
%O A154017 0,1
%A A154017 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154016
%S A154016 7,7,5,5,2,3,8,7,0,0,7,6,9,8,0,1,5,0,8,7,2,3,9,8,7,2,1,4,6,8,8,3,7,2,9,
%T A154016 3,6,6,1,3,4,7,2,5,8,8,8,7,7,5,2,4,8,4,6,9,3,5,1,6,4,3,0,5,8,1,6,1,8,6,
%U A154016 2,5,5,8,6,7,0,6,1,1,4,1,0,8,7,8,1,6,5,4,3,9,5,7,6,2,8,3,0
%N A154016 Decimal expansion of log_17 (9).
%e A154016 .77552387007698015087239872146883729366134725888775248469351...
%K A154016 nonn,cons,new
%O A154016 0,1
%A A154016 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154015
%S A154015 8,1,1,3,6,7,7,4,2,1,6,4,4,2,5,7,8,8,7,6,5,8,0,9,9,9,3,2,0,2,7,8,5,0,5,
%T A154015 8,9,9,9,7,3,5,5,5,6,5,3,2,5,6,0,8,5,4,8,5,2,6,9,4,0,5,2,3,6,2,3,4,2,3,
%U A154015 4,6,5,7,8,1,4,5,5,9,2,7,6,1,2,2,9,5,8,2,2,2,7,1,0,8,5,1,6
%N A154015 Decimal expansion of log_15 (9).
%e A154015 .81136774216442578876580999320278505899973555653256085485269...
%K A154015 nonn,cons,new
%O A154015 0,1
%A A154015 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154014
%S A154014 8,3,2,5,7,9,3,2,7,7,3,1,5,9,8,4,2,9,0,7,3,0,8,1,3,8,4,6,8,5,1,0,3,4,5,
%T A154014 7,9,7,3,5,9,7,9,8,7,4,4,8,8,3,1,8,3,3,4,9,2,8,1,2,4,7,5,3,2,8,1,9,9,4,
%U A154014 9,0,3,5,4,2,1,9,7,6,7,7,9,6,4,7,7,1,7,8,0,0,3,3,9,0,8,1,6
%N A154014 Decimal expansion of log_14 (9).
%e A154014 .83257932773159842907308138468510345797359798744883183349281...
%K A154014 nonn,cons,new
%O A154014 0,1
%A A154014 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154013
%S A154013 8,5,6,6,3,4,6,8,2,0,6,2,7,8,9,3,6,1,9,8,1,5,4,8,7,5,5,8,4,1,9,2,9,1,5,
%T A154013 3,8,1,3,2,6,1,8,5,6,7,6,7,3,6,9,2,3,3,9,9,9,6,4,1,1,3,7,9,7,8,5,6,4,2,
%U A154013 4,5,0,4,6,8,0,7,0,7,4,3,9,7,4,7,3,0,3,7,6,2,7,3,5,1,5,6,0
%N A154013 Decimal expansion of log_13 (9).
%e A154013 .85663468206278936198154875584192915381326185676736923399964...
%K A154013 nonn,cons,new
%O A154013 0,1
%A A154013 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154012
%S A154012 8,8,4,2,2,8,2,1,7,3,9,5,4,8,0,6,2,7,2,3,5,8,2,3,6,7,5,8,4,8,4,5,7,5,8,
%T A154012 7,5,8,0,8,2,2,6,4,9,6,1,4,1,0,7,7,2,8,1,0,9,2,1,5,9,8,6,3,6,6,8,9,3,9,
%U A154012 7,9,0,3,8,1,2,9,7,6,3,6,7,7,2,1,1,1,3,0,5,9,8,5,4,7,5,3,7
%N A154012 Decimal expansion of log_12 (9).
%e A154012 .88422821739548062723582367584845758758082264961410772810921...
%K A154012 nonn,cons,new
%O A154012 0,1
%A A154012 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154011
%S A154011 9,1,6,3,1,3,8,1,9,9,8,2,6,5,2,4,4,4,9,6,4,4,3,6,4,6,7,7,8,5,5,0,5,2,3,
%T A154011 7,8,4,9,2,3,8,7,7,1,2,4,9,6,3,4,6,5,7,3,2,4,6,3,8,9,4,4,4,5,4,5,9,7,6,
%U A154011 0,5,2,4,9,0,2,2,5,2,8,8,8,8,9,1,2,0,9,6,9,6,9,1,7,1,0,2,7
%N A154011 Decimal expansion of log_11 (9).
%e A154011 .91631381998265244496443646778550523784923877124963465732463...
%K A154011 nonn,cons,new
%O A154011 0,1
%A A154011 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154010
%S A154010 1,0,5,6,6,4,1,6,6,7,1,4,7,4,3,7,4,5,4,3,0,2,4,9,2,6,2,9,2,9,8,5,4,4,3,
%T A154010 3,9,1,7,3,2,0,9,6,0,5,1,2,8,3,2,0,7,0,6,9,7,0,5,0,1,7,6,9,6,9,4,0,6,5,
%U A154010 4,8,5,1,9,6,2,3,9,0,4,1,6,8,1,5,2,0,3,1,6,6,1,2,0,5,8,8,2
%N A154010 Decimal expansion of log_8 (9).
%e A154010 1.0566416671474374543024926292985443391732096051283207069705...
%K A154010 nonn,cons,new
%O A154010 1,3
%A A154010 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154009
%S A154009 1,2,2,6,2,9,4,3,8,5,5,3,0,9,1,6,8,2,6,2,5,9,5,0,7,7,2,3,0,6,4,3,5,8,2,
%T A154009 4,7,0,6,9,7,1,6,2,8,1,0,8,5,7,9,3,1,4,3,2,2,1,0,1,0,1,4,2,3,4,6,7,1,5,
%U A154009 9,6,2,9,1,8,5,5,4,3,9,2,3,3,6,6,9,5,3,9,9,4,1,0,3,6,7,9,9
%N A154009 Decimal expansion of log_6 (9).
%e A154009 1.2262943855309168262595077230643582470697162810857931432210...
%K A154009 nonn,cons,new
%O A154009 1,2
%A A154009 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154008
%S A154008 1,3,6,5,2,1,2,3,8,8,9,7,1,9,7,0,5,9,0,2,6,9,1,3,2,7,1,8,5,4,2,1,0,4,5,
%T A154008 0,6,0,4,9,3,3,8,7,9,9,7,4,6,3,3,4,4,1,9,3,2,0,1,1,3,3,8,2,9,8,7,4,9,2,
%U A154008 3,2,5,8,5,3,8,2,6,5,5,4,6,7,3,9,0,8,4,4,1,8,4,4,6,4,0,4,8
%N A154008 Decimal expansion of log_5 (9).
%e A154008 1.3652123889719705902691327185421045060493387997463344193201...
%K A154008 nonn,cons,new
%O A154008 1,2
%A A154008 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154007
%S A154007 6,5,4,3,1,2,8,7,5,9,5,6,5,9,4,6,7,7,6,8,8,0,1,3,4,1,9,3,3,0,1,6,5,1,6,
%T A154007 5,8,8,2,9,8,1,2,7,6,4,9,8,4,9,9,3,0,2,8,4,4,2,1,4,4,6,9,3,9,2,5,5,2,7,
%U A154007 1,4,4,5,0,2,9,7,7,0,5,2,9,3,9,7,5,3,1,4,2,5,6,4,6,6,6,4,2
%N A154007 Decimal expansion of log_24 (8).
%e A154007 .65431287595659467768801341933016516588298127649849930284421...
%K A154007 nonn,cons,new
%O A154007 0,1
%A A154007 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A154006
%S A154006 6,6,3,1,9,4,1,8,8,3,7,2,5,1,1,2,3,8,4,4,9,3,8,8,1,6,2,2,8,6,3,0,0,5,4,
%T A154006 4,5,4,0,2,1,7,3,1,1,0,2,9,6,6,9,9,6,2,0,8,4,1,7,7,7,0,3,9,9,3,6,7,3,4,
%U A154006 6,8,2,8,0,6,6,7,2,8,8,0,1,4,9,5,2,5,0,1,7,0,0,5,4,4,8,7,7
%N A154006 Decimal expansion of log_23 (8).
%e A154006 .66319418837251123844938816228630054454021731102966996208417...
%K A154006 nonn,cons,new
%O A154006 0,1
%A A154006 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153971
%S A153971 6,7,2,7,3,1,4,7,2,6,5,2,7,2,6,3,1,8,4,3,2,6,8,7,0,1,5,2,1,0,4,4,1,4,1,
%T A153971 2,6,9,3,7,3,8,6,4,7,3,2,6,6,6,6,0,2,9,1,7,7,2,8,5,1,3,3,1,9,5,3,4,3,5,
%U A153971 9,0,0,1,9,2,0,4,2,7,1,7,5,2,7,3,8,4,3,0,7,9,2,1,1,1,5,9,6
%N A153971 Decimal expansion of log_22 (8).
%e A153971 .67273147265272631843268701521044141269373864732666602917728...
%K A153971 nonn,cons,new
%O A153971 0,1
%A A153971 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153895
%S A153895 6,8,3,0,1,0,7,4,6,0,9,0,8,5,8,9,9,3,9,4,6,2,2,7,9,1,6,3,0,2,6,7,2,9,8,
%T A153895 6,9,2,3,1,9,6,7,7,3,7,2,3,9,6,9,8,8,8,5,0,1,2,2,4,8,7,0,1,4,6,8,2,6,0,
%U A153895 5,2,7,7,0,5,6,4,3,0,2,7,4,8,6,5,3,4,4,4,5,8,0,2,0,2,2,6,6
%N A153895 Decimal expansion of log_21 (8).
%e A153895 .68301074609085899394622791630267298692319677372396988850122...
%K A153895 nonn,cons,new
%O A153895 0,1
%A A153895 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153872
%S A153872 6,9,4,1,3,4,6,3,9,4,7,9,2,7,7,5,2,2,7,9,1,0,9,3,1,0,3,2,9,2,9,2,1,4,8,
%T A153872 7,6,7,2,8,9,6,5,2,2,1,2,0,6,9,7,5,8,5,5,1,8,8,5,3,3,8,2,3,4,0,5,7,3,6,
%U A153872 6,2,0,9,0,4,7,5,1,5,4,1,4,1,8,9,6,7,5,2,1,3,4,2,6,1,7,7,7
%N A153872 Decimal expansion of log_20 (8).
%e A153872 .69413463947927752279109310329292148767289652212069758551885...
%K A153872 nonn,cons,new
%O A153872 0,1
%A A153872 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153871
%S A153871 7,0,6,2,2,6,7,4,0,0,9,9,9,1,4,7,0,9,3,4,0,8,9,6,3,8,0,1,1,0,5,2,5,5,6,
%T A153871 1,5,0,6,2,2,0,3,2,9,8,8,3,4,4,8,1,4,1,8,6,4,3,9,7,1,0,5,5,0,8,5,7,1,9,
%U A153871 0,6,3,9,6,1,6,3,4,4,5,2,5,7,3,2,0,1,3,7,6,2,4,3,5,0,9,0,9
%N A153871 Decimal expansion of log_19 (8).
%e A153871 .70622674009991470934089638011052556150622032988344814186439...
%K A153871 nonn,cons,new
%O A153871 0,1
%A A153871 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153870
%S A153870 7,1,9,4,3,7,3,9,9,7,0,4,3,9,4,3,3,4,2,0,7,0,5,2,4,9,4,7,3,1,5,6,9,1,8,
%T A153870 5,3,0,4,5,3,3,7,9,0,0,5,7,2,1,1,6,9,7,9,3,5,9,3,4,7,0,2,1,4,4,7,3,8,7,
%U A153870 1,7,2,2,9,5,6,8,6,3,4,5,5,1,9,6,6,9,2,4,4,4,0,4,2,3,3,7,3
%N A153870 Decimal expansion of log_18 (8).
%e A153870 .71943739970439433420705249473156918530453379005721169793593...
%K A153870 nonn,cons,new
%O A153870 0,1
%A A153870 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153858
%S A153858 7,3,3,9,5,1,6,2,6,3,5,4,6,7,8,0,9,1,1,6,9,2,8,4,4,7,3,6,9,5,9,3,3,4,2,
%T A153858 2,1,8,2,7,8,2,8,9,6,8,2,5,0,9,1,0,9,3,3,5,9,0,5,1,1,7,7,5,8,1,5,9,1,9,
%U A153858 3,3,4,7,1,1,5,8,0,5,7,8,4,7,8,2,9,5,5,6,4,1,4,4,0,0,9,2,3
%N A153858 Decimal expansion of log_17 (8).
%e A153858 .73395162635467809116928447369593342218278289682509109335905...
%K A153858 nonn,cons,new
%O A153858 0,1
%A A153858 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153857
%S A153857 7,6,7,8,7,4,0,7,4,4,2,9,4,4,6,4,6,8,1,6,3,0,3,3,0,3,6,5,9,4,4,0,6,8,1,
%T A153857 1,2,1,4,8,2,5,6,3,9,2,7,6,7,0,3,4,2,6,8,0,5,5,4,6,2,9,2,7,8,8,8,5,7,6,
%U A153857 5,9,3,1,6,5,1,7,4,8,3,5,4,4,1,8,2,7,5,1,5,5,8,8,5,8,3,8,4
%N A153857 Decimal expansion of log_15 (8).
%e A153857 .76787407442944646816303303659440681121482563927670342680554...
%K A153857 nonn,cons,new
%O A153857 0,1
%A A153857 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153856
%S A153856 7,8,7,9,4,8,6,0,5,1,1,1,5,8,0,6,4,3,9,3,6,7,2,0,6,0,5,6,9,5,2,4,2,1,6,
%T A153856 1,8,0,1,9,8,4,7,8,4,1,2,0,7,5,9,4,2,9,6,7,6,1,2,7,6,9,8,3,2,3,0,8,8,1,
%U A153856 4,9,9,9,2,5,5,2,6,3,8,8,6,2,5,4,7,5,7,7,0,5,4,4,7,5,2,3,8
%N A153856 Decimal expansion of log_14 (8).
%e A153856 .78794860511158064393672060569524216180198478412075942967612...
%K A153856 nonn,cons,new
%O A153856 0,1
%A A153856 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153855
%S A153855 8,1,0,7,1,4,4,6,3,2,8,1,9,5,9,2,2,3,8,8,2,3,2,4,0,1,0,3,5,1,9,2,6,8,8,
%T A153855 3,1,9,5,9,3,2,6,0,6,9,4,1,0,4,3,4,4,8,2,0,8,3,4,7,4,4,2,0,2,1,0,2,7,0,
%U A153855 8,1,2,0,3,3,5,9,3,6,0,9,0,9,2,4,8,6,9,8,1,2,5,3,8,1,5,2,4
%N A153855 Decimal expansion of log_13 (8).
%e A153855 .81071446328195922388232401035192688319593260694104344820834...
%K A153855 nonn,cons,new
%O A153855 0,1
%A A153855 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153813
%S A153813 8,3,6,8,2,8,8,3,6,9,5,3,3,8,9,5,2,9,5,7,3,1,3,2,2,4,3,1,1,3,6,5,6,8,0,
%T A153813 9,3,1,4,3,8,3,0,1,2,7,8,9,4,1,9,2,0,3,9,1,8,0,8,8,0,1,0,2,2,4,8,2,9,5,
%U A153813 1,5,7,2,1,4,0,2,6,7,7,2,4,2,0,9,1,6,5,2,0,5,1,0,8,9,3,4,6
%N A153813 Decimal expansion of log_12 (8).
%e A153813 .83682883695338952957313224311365680931438301278941920391808...
%K A153813 nonn,cons,new
%O A153813 0,1
%A A153813 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153791
%S A153791 8,6,7,1,9,4,4,7,8,9,5,3,6,6,3,5,7,7,7,9,8,6,3,3,0,2,3,1,0,0,7,9,0,6,9,
%T A153791 8,5,7,3,8,8,3,8,4,7,9,5,7,0,8,8,0,1,0,8,7,9,0,2,4,7,0,3,3,9,5,5,9,4,7,
%U A153791 5,0,6,7,0,7,4,7,3,1,5,7,9,8,9,3,1,2,7,4,6,1,7,5,9,3,4,4,6
%N A153791 Decimal expansion of log_11 (8).
%e A153791 .86719447895366357779863302310079069857388384795708801087902...
%K A153791 nonn,cons,new
%O A153791 0,1
%A A153791 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153790
%S A153790 9,0,3,0,8,9,9,8,6,9,9,1,9,4,3,5,8,5,6,4,1,2,1,6,6,8,4,1,7,3,4,7,9,0,8,
%T A153790 0,3,0,4,5,6,9,6,4,4,3,8,6,3,2,5,6,2,3,9,3,1,2,8,2,3,8,3,3,8,1,3,2,4,5,
%U A153790 6,7,8,2,3,2,7,3,5,2,8,4,6,0,7,8,1,7,5,6,3,5,4,5,5,8,5,1,6
%N A153790 Decimal expansion of log_10 (8).
%e A153790 .90308998699194358564121668417347908030456964438632562393128...
%K A153790 nonn,cons,new
%O A153790 0,1
%A A153790 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153756
%S A153756 9,4,6,3,9,4,6,3,0,3,5,7,1,8,6,1,5,5,6,4,9,2,9,0,6,7,1,5,1,4,1,4,1,2,8,
%T A153756 1,4,4,9,3,7,8,4,6,0,1,9,7,8,2,0,6,4,1,8,0,5,9,8,2,4,1,5,7,5,8,0,2,7,8,
%U A153756 0,2,0,7,1,3,7,2,2,0,7,5,9,1,7,5,9,0,3,2,8,2,4,1,7,7,6,1,8
%N A153756 Decimal expansion of log_9 (8).
%e A153756 .94639463035718615564929067151414128144937846019782064180598...
%K A153756 nonn,cons,new
%O A153756 0,1
%A A153756 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153755
%S A153755 1,0,6,8,6,2,1,5,6,1,3,2,4,0,6,6,5,2,9,5,4,2,5,3,1,2,3,4,0,0,3,8,7,1,5,
%T A153755 8,7,8,9,3,2,7,1,4,8,8,3,1,8,4,4,1,1,0,0,1,1,8,7,2,9,3,7,3,3,7,2,6,0,2,
%U A153755 7,4,1,0,7,7,7,7,8,0,3,3,9,9,1,6,2,2,1,9,6,6,4,9,3,1,8,5,8
%N A153755 Decimal expansion of log_7 (8).
%e A153755 1.0686215613240665295425312340038715878932714883184411001187...
%K A153755 nonn,cons,new
%O A153755 1,3
%A A153755 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153754
%S A153754 1,1,6,0,5,5,8,4,2,1,7,0,3,6,2,4,7,6,0,6,1,0,7,3,8,4,1,5,4,0,3,4,6,2,6,
%T A153754 2,9,3,9,5,4,2,5,5,7,8,3,7,1,3,1,0,2,8,5,1,6,8,4,8,4,7,8,6,4,7,9,9,2,6,
%U A153754 0,5,5,6,2,2,1,6,8,4,1,1,4,9,4,9,5,6,9,0,0,8,8,4,4,4,8,0,1
%N A153754 Decimal expansion of log_6 (8).
%e A153754 1.1605584217036247606107384154034626293954255783713102851684...
%K A153754 nonn,cons,new
%O A153754 1,3
%A A153754 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153739
%S A153739 1,2,9,2,0,2,9,6,7,4,2,2,0,1,7,9,1,5,2,0,1,0,3,1,9,7,0,6,2,9,1,8,9,6,8,
%T A153739 9,6,2,0,9,3,7,5,7,9,6,2,3,9,2,8,1,3,4,7,9,6,5,9,2,8,1,1,3,8,8,1,9,8,6,
%U A153739 2,4,7,6,1,3,6,5,6,5,1,8,2,5,1,0,9,4,2,9,8,3,3,5,8,0,0,9,2
%N A153739 Decimal expansion of log_5 (8).
%e A153739 1.2920296742201791520103197062918968962093757962392813479659...
%K A153739 nonn,cons,new
%O A153739 1,2
%A A153739 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153736
%S A153736 6,1,2,2,9,6,1,5,7,6,2,7,4,7,0,8,7,8,6,5,7,9,0,5,2,2,5,1,2,3,4,3,0,5,7,
%T A153736 1,2,0,6,6,4,1,3,9,5,8,1,3,6,1,9,4,1,7,5,4,7,4,9,8,3,9,0,6,1,0,7,6,9,2,
%U A153736 2,1,9,2,9,6,1,5,9,8,5,1,5,2,1,8,7,2,2,2,3,4,1,9,5,4,8,8,9
%N A153736 Decimal expansion of log_24 (7).
%e A153736 .61229615762747087865790522512343057120664139581361941754749...
%K A153736 nonn,cons,new
%O A153736 0,1
%A A153736 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153735
%S A153735 6,2,0,6,0,7,1,5,6,3,3,5,8,5,5,7,6,8,0,1,4,3,6,8,4,2,7,0,4,9,4,7,9,5,5,
%T A153735 1,7,5,9,9,5,3,8,5,3,2,5,1,9,1,6,5,3,6,5,3,9,4,1,2,0,3,8,8,9,0,7,3,5,3,
%U A153735 0,9,0,2,1,9,4,9,3,8,6,3,5,2,2,3,7,9,8,6,2,6,7,7,1,4,5,1,5
%N A153735 Decimal expansion of log_23 (7).
%e A153735 .62060715633585576801436842704947955175995385325191653653941...
%K A153735 nonn,cons,new
%O A153735 0,1
%A A153735 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153633
%S A153633 6,2,9,5,3,2,0,0,3,6,5,8,2,3,0,5,7,4,2,6,7,0,7,5,0,3,6,0,5,7,9,7,4,5,5,
%T A153633 0,4,2,9,6,8,7,5,9,5,7,6,5,4,7,7,3,6,2,0,2,0,8,2,1,1,6,1,4,7,1,5,1,8,5,
%U A153633 3,8,8,6,3,3,8,6,8,2,8,9,3,4,0,0,5,8,2,2,7,1,5,3,3,6,3,0,1
%N A153633 Decimal expansion of log_22 (7).
%e A153633 .62953200365823057426707503605797455042968759576547736202082...
%K A153633 nonn,cons,new
%O A153633 0,1
%A A153633 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153632
%S A153632 6,3,9,1,5,1,1,9,3,2,8,5,4,6,9,8,2,6,7,5,4,9,1,6,2,0,3,4,9,5,6,9,4,7,3,
%T A153632 9,9,3,5,6,1,3,5,2,0,2,5,1,2,4,2,3,5,2,3,4,0,4,1,1,8,6,2,9,3,8,5,3,0,0,
%U A153632 5,1,8,1,8,7,2,4,0,2,1,0,9,9,6,0,6,9,1,1,1,3,2,9,0,6,7,4,8
%N A153632 Decimal expansion of log_21 (7).
%e A153632 .63915119328546982675491620349569473993561352025124235234041...
%K A153632 nonn,cons,new
%O A153632 0,1
%A A153632 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153630
%S A153630 6,4,9,5,6,0,7,6,5,5,7,0,9,4,3,4,2,5,6,5,4,4,3,3,1,1,3,5,5,7,6,0,3,3,0,
%T A153630 9,7,0,8,2,5,8,5,4,1,6,3,7,6,7,8,7,5,3,2,1,9,4,2,5,1,5,9,5,7,3,4,4,4,0,
%U A153630 4,3,9,3,9,5,2,9,7,6,7,0,7,2,4,0,4,7,0,0,7,4,5,0,5,6,6,0,4
%N A153630 Decimal expansion of log_20 (7).
%e A153630 .64956076557094342565443311355760330970825854163767875321942...
%K A153630 nonn,cons,new
%O A153630 0,1
%A A153630 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153629
%S A153629 6,6,0,8,7,6,3,7,1,6,3,6,0,6,3,9,6,4,0,2,1,1,5,7,3,5,2,1,1,1,9,4,4,8,8,
%T A153629 8,5,8,1,3,4,3,2,0,9,4,8,0,7,0,7,5,6,3,8,8,9,6,1,2,0,9,2,8,6,7,7,7,5,1,
%U A153629 9,5,2,6,7,3,0,0,9,6,9,5,8,0,9,4,0,1,8,2,7,3,6,8,8,1,6,3,4
%N A153629 Decimal expansion of log_19 (7).
%e A153629 .66087637163606396402115735211194488858134320948070756388961...
%K A153629 nonn,cons,new
%O A153629 0,1
%A A153629 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153628
%S A153628 6,7,3,2,3,8,7,0,8,3,9,0,8,1,8,4,4,2,8,1,1,8,0,8,2,4,8,0,4,4,4,3,3,8,5,
%T A153628 1,0,4,5,8,5,8,4,0,2,7,7,2,1,5,8,5,2,5,0,0,8,7,8,2,2,5,6,1,1,0,6,2,6,5,
%U A153628 7,6,8,1,7,4,5,0,2,0,3,1,1,4,5,8,7,2,9,5,7,6,0,5,3,9,2,6,5
%N A153628 Decimal expansion of log_18 (7).
%e A153628 .67323870839081844281180824804443385104585840277215852500878...
%K A153628 nonn,cons,new
%O A153628 0,1
%A A153628 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153627
%S A153627 6,8,6,8,2,0,9,0,3,5,9,9,6,6,3,0,2,8,4,3,7,1,3,2,8,3,2,7,8,1,2,9,9,4,3,
%T A153627 8,9,4,5,1,7,0,9,4,1,5,7,1,3,0,0,2,8,2,4,6,5,3,2,5,5,8,6,9,5,3,1,6,8,6,
%U A153627 1,0,7,2,2,2,8,2,0,3,9,0,0,1,5,4,7,4,4,9,7,1,4,6,2,7,4,8,3
%N A153627 Decimal expansion of log_17 (7).
%e A153627 .68682090359966302843713283278129943894517094157130028246532...
%K A153627 nonn,cons,new
%O A153627 0,1
%A A153627 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153626
%S A153626 7,0,1,8,3,8,7,3,0,5,1,4,4,0,1,0,2,6,8,6,0,4,9,2,3,2,9,3,0,7,9,5,7,7,0,
%T A153626 2,1,6,0,2,5,6,6,5,6,4,9,1,5,3,5,1,9,5,9,1,9,3,2,2,9,3,1,0,1,7,5,8,0,2,
%U A153626 1,2,2,1,5,5,4,8,2,4,6,6,2,4,4,6,5,2,4,9,7,9,2,5,5,2,6,9,6
%N A153626 Decimal expansion of log_16 (7).
%e A153626 .70183873051440102686049232930795770216025665649153519591932...
%K A153626 nonn,cons,new
%O A153626 0,1
%A A153626 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153625
%S A153625 7,1,8,5,6,5,0,2,0,7,8,9,9,7,7,8,6,1,6,0,6,1,1,4,5,5,7,4,7,6,7,8,5,3,3,
%T A153625 8,4,8,3,4,4,0,3,5,9,9,9,5,8,0,9,0,1,3,4,6,8,2,1,8,1,7,9,3,7,0,9,7,6,1,
%U A153625 8,7,9,3,1,1,8,9,8,4,9,1,4,3,1,2,6,2,8,3,3,2,9,4,7,1,0,2,0
%N A153625 Decimal expansion of log_15 (7).
%e A153625 .71856502078997786160611455747678533848344035999580901346821...
%K A153625 nonn,cons,new
%O A153625 0,1
%A A153625 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153624
%S A153624 7,3,7,3,5,0,4,6,4,9,6,2,8,0,6,4,5,2,0,2,1,0,9,3,1,3,1,4,3,4,9,1,9,2,7,
%T A153624 9,3,9,9,3,3,8,4,0,5,2,9,3,0,8,0,1,9,0,1,0,7,9,5,7,4,3,3,8,9,2,3,0,3,9,
%U A153624 5,0,0,0,2,4,8,2,4,5,3,7,1,2,4,8,4,1,4,0,9,8,1,8,4,1,5,8,7
%N A153624 Decimal expansion of log_14 (7).
%e A153624 .73735046496280645202109313143491927939933840529308019010795...
%K A153624 nonn,cons,new
%O A153624 0,1
%A A153624 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153623
%S A153623 7,5,8,6,5,4,4,1,2,9,5,9,2,9,8,9,9,4,6,7,2,3,3,1,5,7,5,7,8,9,7,0,4,3,0,
%T A153623 7,2,0,8,6,5,1,7,7,5,0,8,5,0,8,1,2,9,0,0,0,0,9,8,7,4,5,1,9,6,5,0,5,4,7,
%U A153623 6,0,1,3,1,4,4,3,7,4,2,6,6,3,3,8,8,0,7,0,9,2,1,9,1,6,4,1,8
%N A153623 Decimal expansion of log_13 (7).
%e A153623 .75865441295929899467233157578970430720865177508508129000098...
%K A153623 nonn,cons,new
%O A153623 0,1
%A A153623 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153622
%S A153622 7,8,3,0,9,1,8,5,1,4,4,6,9,4,6,1,1,9,5,5,4,9,3,2,8,7,8,6,1,4,8,1,0,6,8,
%T A153622 6,7,6,3,4,8,0,1,2,4,7,4,5,0,9,6,7,6,8,1,7,8,6,4,8,5,7,2,6,0,6,9,1,6,0,
%U A153622 7,0,7,0,3,0,2,4,2,8,2,5,4,0,8,8,9,3,9,5,5,7,9,2,4,4,7,1,5
%N A153622 Decimal expansion of log_12 (7).
%e A153622 .78309185144694611955493287861481068676348012474509676817864...
%K A153622 nonn,cons,new
%O A153622 0,1
%A A153622 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153621
%S A153621 8,1,1,5,0,7,5,6,2,9,5,7,2,4,8,9,3,9,6,6,7,9,5,0,5,9,2,9,4,0,5,4,1,2,3,
%T A153621 8,0,9,3,9,8,0,7,9,7,9,5,2,9,1,5,8,3,8,3,7,3,2,9,9,5,0,6,0,5,7,3,6,3,1,
%U A153621 6,9,1,1,6,1,3,2,5,0,3,4,4,1,7,6,6,6,9,1,3,0,7,1,8,7,7,9,3
%N A153621 Decimal expansion of log_11 (7).
%e A153621 .81150756295724893966795059294054123809398079795291583837329...
%K A153621 nonn,cons,new
%O A153621 0,1
%A A153621 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153620
%S A153620 8,4,5,0,9,8,0,4,0,0,1,4,2,5,6,8,3,0,7,1,2,2,1,6,2,5,8,5,9,2,6,3,6,1,9,
%T A153620 3,4,8,3,5,7,2,3,9,6,3,2,3,9,6,5,4,0,6,5,0,3,6,3,4,9,5,3,7,1,8,2,5,3,4,
%U A153620 3,9,9,0,2,0,7,9,1,6,6,0,6,6,1,1,1,5,2,7,8,4,7,4,8,8,5,7,3
%N A153620 Decimal expansion of log_10 (7).
%e A153620 .84509804001425683071221625859263619348357239632396540650363...
%K A153620 nonn,cons,new
%O A153620 0,1
%A A153620 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153619
%S A153619 8,8,5,6,2,1,8,7,4,5,8,0,7,1,1,1,3,0,0,3,3,9,6,4,1,5,3,5,4,1,2,2,8,8,5,
%T A153619 9,0,3,3,2,3,5,6,6,7,2,9,7,1,2,1,7,3,9,6,8,4,4,9,6,2,8,8,6,3,9,9,4,3,0,
%U A153619 9,9,3,5,1,4,0,6,1,0,5,4,1,7,1,5,0,4,9,4,6,6,8,7,5,4,4,8,8
%N A153619 Decimal expansion of log_9 (7).
%e A153619 .88562187458071113003396415354122885903323566729712173968449...
%K A153619 nonn,cons,new
%O A153619 0,1
%A A153619 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153618
%S A153618 9,3,5,7,8,4,9,7,4,0,1,9,2,0,1,3,6,9,1,4,7,3,2,3,1,0,5,7,4,3,9,4,3,6,0,
%T A153618 2,8,8,0,3,4,2,2,0,8,6,5,5,3,8,0,2,6,1,2,2,5,7,6,3,9,0,8,0,2,3,4,4,0,2,
%U A153618 8,2,9,5,4,0,6,4,3,2,8,8,3,2,6,2,0,3,3,3,0,5,6,7,3,6,9,2,8
%N A153618 Decimal expansion of log_8 (7).
%e A153618 .93578497401920136914732310574394360288034220865538026122576...
%K A153618 nonn,cons,new
%O A153618 0,1
%A A153618 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153617
%S A153617 1,0,8,6,0,3,3,1,3,2,5,0,1,6,9,1,8,4,2,9,8,6,0,4,2,0,5,0,9,2,7,8,2,1,3,
%T A153617 3,2,9,1,8,7,8,0,9,5,5,2,0,1,1,9,2,9,9,4,8,8,7,1,0,2,4,6,0,2,7,6,5,9,4,
%U A153617 6,4,5,8,7,2,1,4,5,6,5,0,9,9,0,3,4,1,6,6,1,1,8,9,1,4,4,0,3
%N A153617 Decimal expansion of log_6 (7).
%e A153617 1.0860331325016918429860420509278213329187809552011929948871...
%K A153617 nonn,cons,new
%O A153617 1,3
%A A153617 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153616
%S A153616 1,2,0,9,0,6,1,9,5,5,1,2,2,1,6,7,5,5,6,7,6,3,3,1,6,3,4,5,5,4,7,3,6,0,0,
%T A153616 7,1,1,1,6,5,5,5,9,2,9,7,1,0,8,3,3,1,2,8,7,0,6,2,3,6,2,0,0,8,5,2,8,7,8,
%U A153616 2,0,0,9,9,7,4,9,9,9,8,6,5,9,9,0,1,7,3,1,8,9,7,1,6,7,5,1,7
%N A153616 Decimal expansion of log_5 (7).
%e A153616 1.2090619551221675567633163455473600711165559297108331287062...
%K A153616 nonn,cons,new
%O A153616 1,2
%A A153616 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153615
%S A153615 1,4,0,3,6,7,7,4,6,1,0,2,8,8,0,2,0,5,3,7,2,0,9,8,4,6,5,8,6,1,5,9,1,5,4,
%T A153615 0,4,3,2,0,5,1,3,3,1,2,9,8,3,0,7,0,3,9,1,8,3,8,6,4,5,8,6,2,0,3,5,1,6,0,
%U A153615 4,2,4,4,3,1,0,9,6,4,9,3,2,4,8,9,3,0,4,9,9,5,8,5,1,0,5,3,9
%N A153615 Decimal expansion of log_4 (7).
%e A153615 1.4036774610288020537209846586159154043205133129830703918386...
%K A153615 nonn,cons,new
%O A153615 1,2
%A A153615 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153614
%S A153614 5,6,3,7,9,1,4,1,6,0,2,8,9,3,6,8,8,1,5,4,1,3,2,4,3,8,7,1,1,3,2,2,3,2,2,
%T A153614 2,7,4,4,6,7,9,1,4,9,0,0,1,0,0,0,4,6,4,7,7,0,5,2,3,6,8,7,0,7,1,6,3,1,5,
%U A153614 2,3,6,9,9,8,0,1,5,2,9,8,0,4,0,1,6,4,5,7,1,6,2,3,5,5,5,7,1
%N A153614 Decimal expansion of log_24 (6).
%e A153614 .56379141602893688154132438711322322274467914900100046477052...
%K A153614 nonn,cons,new
%O A153614 0,1
%A A153614 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153613
%S A153613 5,7,1,4,4,4,0,3,5,8,7,9,7,1,4,7,2,3,5,5,6,4,1,9,4,6,2,7,3,9,4,0,4,9,4,
%T A153613 6,7,0,3,2,3,8,9,5,6,1,9,1,6,9,4,9,9,6,0,2,2,1,8,4,9,0,4,2,9,9,6,7,6,6,
%U A153613 3,1,6,1,6,3,9,9,3,3,8,0,5,7,7,9,5,7,7,0,4,7,3,7,9,2,9,2,9
%N A153613 Decimal expansion of log_23 (6).
%e A153613 .57144403587971472355641946273940494670323895619169499602218...
%K A153613 nonn,cons,new
%O A153613 0,1
%A A153613 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153612
%S A153612 5,7,9,6,6,1,8,7,6,6,2,0,7,3,9,1,7,1,9,5,7,8,4,8,4,0,9,1,8,5,6,4,4,8,5,
%T A153612 8,4,1,8,0,9,1,2,2,4,2,7,3,4,3,8,7,4,6,0,3,1,9,7,4,9,3,8,9,5,5,7,7,3,2,
%U A153612 4,8,0,3,8,4,9,4,5,3,5,2,9,3,1,8,5,1,6,8,6,8,5,8,1,8,4,9,9
%N A153612 Decimal expansion of log_22 (6).
%e A153612 .57966187662073917195784840918564485841809122427343874603197...
%K A153612 nonn,cons,new
%O A153612 0,1
%A A153612 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153611
%S A153611 5,8,8,5,1,9,0,5,5,4,1,1,4,8,3,1,7,1,2,2,7,1,5,9,7,6,8,6,0,5,1,9,6,2,5,
%T A153611 5,7,0,5,4,5,2,0,7,0,9,9,0,0,8,0,9,4,3,8,2,6,6,6,3,0,9,3,7,7,7,0,7,8,6,
%U A153611 3,2,4,3,8,1,3,0,7,4,6,4,8,3,2,7,7,5,7,0,3,9,3,8,2,7,3,3,9
%N A153611 Decimal expansion of log_21 (6).
%e A153611 .58851905541148317122715976860519625570545207099008094382666...
%K A153611 nonn,cons,new
%O A153611 0,1
%A A153611 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153610
%S A153610 5,9,8,1,0,4,0,0,4,5,0,1,8,4,3,8,0,3,1,7,6,5,0,4,8,4,3,7,5,6,9,7,3,1,4,
%T A153610 9,4,8,6,7,3,3,9,3,8,3,0,5,8,9,7,9,3,0,1,2,8,6,0,5,3,7,1,3,8,8,4,7,1,2,
%U A153610 5,0,9,6,1,7,2,7,4,9,4,0,9,2,7,7,1,5,2,1,8,2,9,1,6,0,3,4,1
%N A153610 Decimal expansion of log_20 (6).
%e A153610 .59810400450184380317650484375697314948673393830589793012860...
%K A153610 nonn,cons,new
%O A153610 0,1
%A A153610 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153609
%S A153609 6,0,8,5,2,3,2,1,3,3,8,8,2,7,5,1,8,5,3,2,5,1,9,7,8,2,8,1,4,2,0,3,4,8,9,
%T A153609 0,0,6,1,0,2,3,5,2,4,8,7,9,9,5,2,4,0,5,2,7,6,9,9,8,6,1,0,4,4,9,7,3,7,4,
%U A153609 9,3,8,5,5,1,0,1,7,9,8,7,7,6,4,7,0,0,9,5,7,9,1,4,7,3,8,0,6
%N A153609 Decimal expansion of log_19 (6).
%e A153609 .60852321338827518532519782814203489006102352487995240527699...
%K A153609 nonn,cons,new
%O A153609 0,1
%A A153609 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153608
%S A153608 6,1,9,9,0,6,2,3,3,2,8,4,0,6,5,7,2,2,3,6,7,8,4,2,0,8,2,4,5,5,2,6,1,5,3,
%T A153608 0,8,8,4,0,8,8,9,6,5,0,0,9,5,3,5,2,8,2,9,8,9,3,2,2,4,5,0,3,5,7,4,5,6,4,
%U A153608 5,2,8,7,1,5,9,4,7,7,2,4,2,5,3,2,7,8,2,0,7,4,0,0,7,0,5,6,2
%N A153608 Decimal expansion of log_18 (6).
%e A153608 .61990623328406572236784208245526153088408896500953528298932...
%K A153608 nonn,cons,new
%O A153608 0,1
%A A153608 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153607
%S A153607 6,3,2,4,1,2,4,7,7,1,5,6,7,1,6,1,0,5,8,2,5,9,6,0,8,5,1,9,6,6,3,9,6,4,5,
%T A153607 4,2,2,4,9,3,4,5,9,5,0,5,2,2,3,9,9,4,0,1,3,3,1,0,8,6,0,7,8,1,8,0,0,6,6,
%U A153607 2,3,9,5,0,4,0,5,7,4,3,0,0,3,6,6,7,3,4,6,0,0,2,6,8,1,7,2,2
%N A153607 Decimal expansion of log_17 (6).
%e A153607 .63241247715671610582596085196639645422493459505223994013310...
%K A153607 nonn,cons,new
%O A153607 0,1
%A A153607 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153606
%S A153606 6,4,6,2,4,0,6,2,5,1,8,0,2,8,9,0,4,5,3,6,3,4,3,4,7,3,5,9,8,6,9,5,4,1,2,
%T A153606 7,1,8,9,9,5,3,6,0,1,9,2,3,1,2,0,2,6,5,1,1,3,9,3,8,1,6,3,6,3,5,2,7,4,5,
%U A153606 5,6,9,4,8,5,8,9,6,4,0,6,3,0,5,7,0,1,1,8,7,2,9,5,2,2,0,6,0
%N A153606 Decimal expansion of log_16 (6).
%e A153606 .64624062518028904536343473598695412718995360192312026511393...
%K A153606 nonn,cons,new
%O A153606 0,1
%A A153606 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153605
%S A153605 6,6,1,6,4,1,8,9,5,8,9,2,0,2,8,3,8,3,7,7,0,5,8,2,6,7,5,4,6,6,1,9,4,7,9,
%T A153605 9,9,0,4,8,0,9,6,5,8,0,2,5,1,8,1,5,6,9,6,9,4,8,6,2,4,5,7,1,1,0,7,9,0,3,
%U A153605 9,3,0,6,1,2,4,5,2,9,0,8,9,5,3,4,2,3,7,4,9,6,6,5,0,7,0,5,2
%N A153605 Decimal expansion of log_15 (6).
%e A153605 .66164189589202838377058267546619479990480965802518156969486...
%K A153605 nonn,cons,new
%O A153605 0,1
%A A153605 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153604
%S A153604 6,7,8,9,3,9,1,9,8,9,0,2,9,9,2,7,6,2,5,1,5,4,4,7,5,6,0,9,0,7,6,3,2,4,4,
%T A153604 9,5,8,7,4,6,0,5,8,8,4,3,1,3,3,5,7,2,6,6,3,8,4,4,8,8,0,3,7,7,1,7,9,5,7,
%U A153604 9,5,1,7,4,6,2,7,4,3,0,1,8,5,7,5,4,4,4,8,0,1,9,8,5,3,8,2,1
%N A153604 Decimal expansion of log_14 (6).
%e A153604 .67893919890299276251544756090763244958746058843133572663844...
%K A153604 nonn,cons,new
%O A153604 0,1
%A A153604 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153603
%S A153603 6,9,8,5,5,5,4,9,5,4,5,8,7,1,4,4,2,2,2,8,4,8,8,2,3,8,1,3,7,1,6,0,6,8,7,
%T A153603 1,3,0,5,2,7,5,1,3,0,6,9,7,3,6,5,7,6,6,4,0,2,6,0,3,0,4,9,6,6,2,9,5,7,8,
%U A153603 1,6,2,5,7,8,5,6,6,5,7,5,0,1,8,1,9,4,1,8,1,8,8,8,0,2,9,5,4
%N A153603 Decimal expansion of log_13 (6).
%e A153603 .69855549545871442228488238137160687130527513069736576640260...
%K A153603 nonn,cons,new
%O A153603 0,1
%A A153603 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153589
%S A153589 7,2,1,0,5,7,0,5,4,3,4,8,8,7,0,1,5,6,8,0,8,9,5,5,9,1,8,9,6,2,1,1,4,3,9,
%T A153589 6,8,9,5,2,0,5,6,6,2,4,0,3,5,2,6,9,3,2,0,2,7,3,0,3,9,9,6,5,9,1,7,2,3,4,
%U A153589 9,4,7,5,9,5,3,2,4,4,0,9,1,9,3,0,2,7,8,2,6,4,9,6,3,6,8,8,4
%N A153589 Decimal expansion of log_12 (6).
%e A153589 .72105705434887015680895591896211439689520566240352693202730...
%K A153589 nonn,cons,new
%O A153589 0,1
%A A153589 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153586
%S A153586 7,4,7,2,2,1,7,3,6,3,0,9,2,1,4,0,8,1,7,4,8,4,2,9,2,4,1,5,9,3,0,1,6,1,8,
%T A153586 5,1,1,5,9,1,4,0,0,1,6,1,0,5,1,3,3,3,2,2,8,8,6,6,1,0,4,0,0,2,5,8,3,0,3,
%U A153586 8,6,1,8,1,4,2,7,0,3,6,3,7,7,4,3,3,1,4,0,0,2,3,7,8,3,3,2,9
%N A153586 Decimal expansion of log_11 (6).
%e A153586 .74722173630921408174842924159301618511591400161051333228866...
%K A153586 nonn,cons,new
%O A153586 0,1
%A A153586 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153496
%S A153496 7,7,8,1,5,1,2,5,0,3,8,3,6,4,3,6,3,2,5,0,8,7,6,6,7,9,7,9,7,9,6,0,8,3,3,
%T A153496 5,9,6,8,3,1,8,7,4,5,6,5,2,8,0,4,4,0,6,1,4,0,2,9,3,1,0,1,4,3,2,3,3,7,3,
%U A153496 4,2,0,5,8,0,8,5,6,3,2,5,2,9,8,9,5,6,0,7,7,6,5,8,0,2,4,7,3
%N A153496 Decimal expansion of log_10 (6).
%e A153496 .77815125038364363250876679797960833596831874565280440614029...
%K A153496 nonn,cons,new
%O A153496 0,1
%A A153496 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153495
%S A153495 8,1,5,4,6,4,8,7,6,7,8,5,7,2,8,7,1,8,5,4,9,7,6,3,5,5,7,1,7,1,3,8,0,4,2,
%T A153495 7,1,4,9,7,9,2,8,2,0,0,6,5,9,4,0,2,1,3,9,3,5,3,2,7,4,7,1,9,1,9,3,4,2,6,
%U A153495 0,0,6,9,0,4,5,7,4,0,2,5,3,0,5,8,6,3,4,4,2,7,4,7,2,5,8,7,2
%N A153495 Decimal expansion of log_9 (6).
%e A153495 .81546487678572871854976355717138042714979282006594021393532...
%K A153495 nonn,cons,new
%O A153495 0,1
%A A153495 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153493
%S A153493 8,6,1,6,5,4,1,6,6,9,0,7,0,5,2,0,6,0,4,8,4,5,7,9,6,4,7,9,8,2,6,0,5,5,0,
%T A153493 2,9,1,9,9,3,8,1,3,5,8,9,7,4,9,3,6,8,6,8,1,8,5,8,4,2,1,8,1,8,0,3,6,6,0,
%U A153493 7,5,9,3,1,4,5,2,8,5,4,1,7,4,0,9,3,4,9,1,6,3,9,3,6,2,7,4,7
%N A153493 Decimal expansion of log_8 (6).
%e A153493 .86165416690705206048457964798260550291993813589749368681858...
%K A153493 nonn,cons,new
%O A153493 0,1
%A A153493 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153463
%S A153463 9,2,0,7,8,2,2,2,1,1,6,1,6,0,1,7,9,0,3,1,8,7,2,7,2,4,5,1,7,6,1,9,9,0,6,
%T A153463 5,4,4,0,9,8,5,0,7,3,9,5,9,6,0,6,2,9,5,0,8,4,9,8,5,7,2,0,0,9,8,6,1,9,8,
%U A153463 9,4,5,5,9,6,6,8,8,4,3,6,7,4,1,5,5,6,1,0,1,3,4,1,3,4,1,2,2
%N A153463 Decimal expansion of log_7 (6).
%e A153463 .92078222116160179031872724517619906544098507395960629508498...
%K A153463 nonn,cons,new
%O A153463 0,1
%A A153463 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153461
%S A153461 1,1,1,3,2,8,2,7,5,2,5,5,9,3,7,8,3,4,5,8,0,4,6,7,2,9,2,8,0,3,5,0,1,7,8,
%T A153461 8,5,0,9,4,4,6,1,3,3,1,9,5,2,9,2,7,6,5,8,9,8,2,0,3,2,7,2,9,4,5,4,4,0,8,
%U A153461 2,4,5,4,6,4,7,9,8,7,8,3,4,2,0,6,5,2,3,2,0,3,6,7,5,8,7,2,1
%N A153461 Decimal expansion of log_5 (6).
%e A153461 1.1132827525593783458046729280350178850944613319529276589820...
%K A153461 nonn,cons,new
%O A153461 1,4
%A A153461 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153460
%S A153460 1,2,9,2,4,8,1,2,5,0,3,6,0,5,7,8,0,9,0,7,2,6,8,6,9,4,7,1,9,7,3,9,0,8,2,
%T A153460 5,4,3,7,9,9,0,7,2,0,3,8,4,6,2,4,0,5,3,0,2,2,7,8,7,6,3,2,7,2,7,0,5,4,9,
%U A153460 1,1,3,8,9,7,1,7,9,2,8,1,2,6,1,1,4,0,2,3,7,4,5,9,0,4,4,1,2
%N A153460 Decimal expansion of log_4 (6).
%e A153460 1.2924812503605780907268694719739082543799072038462405302278...
%K A153460 nonn,cons,new
%O A153460 1,2
%A A153460 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153459
%S A153459 1,6,3,0,9,2,9,7,5,3,5,7,1,4,5,7,4,3,7,0,9,9,5,2,7,1,1,4,3,4,2,7,6,0,8,
%T A153459 5,4,2,9,9,5,8,5,6,4,0,1,3,1,8,8,0,4,2,7,8,7,0,6,5,4,9,4,3,8,3,8,6,8,5,
%U A153459 2,0,1,3,8,0,9,1,4,8,0,5,0,6,1,1,7,2,6,8,8,5,4,9,4,5,1,7,4
%N A153459 Decimal expansion of log_3 (6).
%e A153459 1.6309297535714574370995271143427608542995856401318804278706...
%K A153459 nonn,cons,new
%O A153459 1,2
%A A153459 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153458
%S A153458 5,0,6,4,2,2,4,8,3,1,7,6,7,2,2,3,0,5,5,1,5,0,9,9,4,1,9,2,0,7,5,8,7,6,2,
%T A153458 7,9,9,1,0,2,2,4,7,6,2,7,8,1,4,9,2,8,6,3,0,9,0,3,2,0,2,8,7,2,0,8,9,1,4,
%U A153458 5,7,1,8,9,8,0,5,5,3,8,2,5,9,2,4,5,5,3,9,2,7,7,0,4,0,6,1,1
%N A153458 Decimal expansion of log_24 (5).
%e A153458 .50642248317672230551509941920758762799102247627814928630903...
%K A153458 nonn,cons,new
%O A153458 0,1
%A A153458 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153457
%S A153457 5,1,3,2,9,6,4,0,6,1,1,6,0,5,1,8,4,4,6,5,8,1,8,3,2,8,0,5,4,0,9,8,7,1,2,
%T A153457 2,3,0,6,4,4,3,0,5,6,4,1,5,3,6,7,4,2,1,2,2,1,6,7,6,4,0,2,4,4,5,0,7,3,8,
%U A153457 2,0,7,8,1,6,1,8,0,1,3,0,5,9,6,5,5,0,0,3,2,3,1,7,0,1,5,1,3
%N A153457 Decimal expansion of log_23 (5).
%e A153457 .51329640611605184465818328054098712230644305641536742122167...
%K A153457 nonn,cons,new
%O A153457 0,1
%A A153457 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153456
%S A153456 5,2,0,6,7,8,0,3,5,5,5,5,7,7,1,5,0,7,8,4,0,4,7,5,6,1,3,9,5,9,3,0,1,9,3,
%T A153456 6,0,2,3,7,1,1,6,8,5,2,7,9,8,4,4,7,7,8,1,9,6,7,9,8,3,9,0,7,4,0,0,6,2,9,
%U A153456 2,2,0,7,8,0,6,6,0,4,7,1,4,8,2,3,3,9,7,2,1,8,7,1,6,2,1,8,8
%N A153456 Decimal expansion of log_22 (5).
%e A153456 .52067803555577150784047561395930193602371168527984477819679...
%K A153456 nonn,cons,new
%O A153456 0,1
%A A153456 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153455
%S A153455 5,2,8,6,3,3,9,4,6,8,1,9,4,4,8,0,6,4,6,3,6,0,5,5,2,5,3,0,5,9,1,1,9,9,1,
%T A153455 4,0,3,8,9,6,5,1,3,1,3,3,6,7,0,0,3,8,6,4,5,9,1,7,5,6,6,1,0,7,0,4,3,8,2,
%U A153455 8,5,1,0,2,1,2,2,5,2,5,6,8,6,9,8,0,3,9,8,9,0,1,3,6,3,9,9,8
%N A153455 Decimal expansion of log_21 (5).
%e A153455 .52863394681944806463605525305911991403896513133670038645917...
%K A153455 nonn,cons,new
%O A153455 0,1
%A A153455 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153454
%S A153454 5,3,7,2,4,3,5,7,3,6,8,0,4,8,1,6,5,1,4,7,2,6,0,4,5,9,7,8,0,4,7,1,9,0,0,
%T A153454 8,2,1,8,0,6,8,9,8,5,2,5,2,8,6,8,2,7,6,3,2,0,7,6,4,4,1,1,7,7,2,9,5,0,8,
%U A153454 9,1,9,3,9,6,8,3,2,3,0,5,7,2,0,6,8,8,3,1,9,1,0,4,9,2,1,4,8
%N A153454 Decimal expansion of log_20 (5).
%e A153454 .53724357368048165147260459780471900821806898525286827632076...
%K A153454 nonn,cons,new
%O A153454 0,1
%A A153454 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153451
%S A153451 5,4,6,6,0,2,5,6,9,7,3,2,9,0,2,4,4,9,6,1,5,4,4,4,5,7,0,8,7,8,6,6,7,4,5,
%T A153451 4,2,0,8,4,3,7,2,5,2,5,9,3,0,5,7,0,5,7,8,9,7,4,1,8,4,8,0,8,3,6,6,0,8,3,
%U A153451 9,4,8,1,7,9,6,9,8,6,1,6,1,5,0,6,4,3,0,1,5,8,9,0,7,7,6,9,9
%N A153451 Decimal expansion of log_19 (5).
%e A153451 .54660256973290244961544457087866745420843725259305705789741...
%K A153451 nonn,cons,new
%O A153451 0,1
%A A153451 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153444
%S A153444 5,5,6,8,2,7,3,0,3,6,2,8,7,8,0,7,1,9,9,9,9,0,6,3,0,7,0,1,0,9,8,4,9,6,0,
%T A153444 2,3,4,7,8,2,8,9,8,5,0,0,8,5,2,7,5,9,4,1,9,3,7,9,2,2,2,8,2,6,6,7,4,6,4,
%U A153444 1,8,2,9,9,5,7,2,0,7,1,5,4,7,5,4,0,5,1,8,1,9,0,0,4,2,8,1,3
%N A153444 Decimal expansion of log_18 (5).
%e A153444 .55682730362878071999906307010984960234782898500852759419379...
%K A153444 nonn,cons,new
%O A153444 0,1
%A A153444 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153430
%S A153430 5,6,8,0,6,0,9,6,7,1,7,3,7,3,2,9,6,8,8,6,5,8,6,0,4,9,8,4,9,4,6,2,0,5,2,
%T A153430 4,8,9,7,5,0,2,0,6,4,3,7,6,4,4,1,2,1,0,9,2,2,5,3,1,9,6,3,5,5,8,2,0,3,2,
%U A153430 7,9,7,2,2,7,1,3,1,2,8,6,1,2,1,6,1,9,2,6,7,9,8,6,8,7,6,6,5
%N A153430 Decimal expansion of log_17 (5).
%e A153430 .56806096717373296886586049849462052489750206437644121092253...
%K A153430 nonn,cons,new
%O A153430 0,1
%A A153430 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153420
%S A153420 5,8,0,4,8,2,0,2,3,7,2,1,8,4,0,5,8,6,9,6,7,5,7,9,8,5,7,3,7,2,3,4,7,5,4,
%T A153420 3,9,6,6,2,0,7,8,4,8,2,5,6,1,4,5,1,5,3,0,1,3,6,8,9,0,9,8,9,5,3,9,8,3,6,
%U A153420 9,4,1,5,2,1,5,6,3,0,3,9,6,2,5,3,4,9,3,5,8,3,9,8,4,2,5,3,8
%N A153420 Decimal expansion of log_16 (5).
%e A153420 .58048202372184058696757985737234754396620784825614515301368...
%K A153420 nonn,cons,new
%O A153420 0,1
%A A153420 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153356
%S A153356 5,9,4,3,1,6,1,2,8,9,1,7,7,8,7,1,0,5,6,1,7,0,9,5,0,0,3,3,9,8,6,0,7,4,7,
%T A153356 0,5,0,0,1,3,2,2,2,1,7,3,3,7,1,9,5,7,2,5,7,3,6,5,2,9,7,3,8,1,8,8,2,8,8,
%U A153356 2,6,7,1,0,9,2,7,2,0,3,6,1,9,3,8,5,2,0,8,8,8,6,4,4,5,7,4,1
%N A153356 Decimal expansion of log_15 (5).
%e A153356 .59431612891778710561709500339860747050013222173371957257365...
%K A153356 nonn,cons,new
%O A153356 0,1
%A A153356 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153314
%S A153314 6,0,9,8,5,3,3,3,4,5,1,1,9,6,2,3,4,2,0,4,5,4,1,2,5,7,0,0,4,7,8,7,0,1,8,
%T A153314 2,5,0,6,9,2,5,9,3,7,3,2,4,9,7,4,8,4,5,2,6,9,5,3,2,8,3,3,6,3,8,8,9,5,5,
%U A153314 1,4,4,0,7,0,8,5,5,2,4,8,9,4,8,1,3,4,0,1,4,9,4,3,4,5,9,2,0
%N A153314 Decimal expansion of log_14 (5).
%e A153314 .60985333451196234204541257004787018250692593732497484526953...
%K A153314 nonn,cons,new
%O A153314 0,1
%A A153314 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153313
%S A153313 6,2,7,4,7,3,5,6,3,0,7,5,3,0,3,3,5,1,6,2,8,3,6,9,6,9,2,8,2,3,9,1,8,4,1,
%T A153313 8,0,8,6,3,6,6,1,2,5,0,1,9,5,4,3,8,7,6,3,1,7,5,8,5,5,9,8,8,6,6,6,3,6,4,
%U A153313 6,8,3,1,5,1,5,3,3,9,0,3,1,8,0,7,2,4,3,2,1,8,9,3,7,1,6,0,0
%N A153313 Decimal expansion of log_13 (5).
%e A153313 .62747356307530335162836969282391841808636612501954387631758...
%K A153313 nonn,cons,new
%O A153313 0,1
%A A153313 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153306
%S A153306 6,4,7,6,8,5,4,6,2,3,7,7,9,9,6,9,7,2,9,2,1,9,4,9,3,4,7,1,2,9,2,0,7,4,0,
%T A153306 0,8,9,6,7,4,1,5,2,4,9,3,7,5,0,8,4,9,1,5,5,8,6,6,5,0,4,5,8,5,4,2,0,5,9,
%U A153306 8,0,5,6,2,2,0,6,7,1,6,1,2,8,9,2,2,5,0,0,6,8,4,4,9,9,6,9,5
%N A153306 Decimal expansion of log_12 (5).
%e A153306 .64768546237799697292194934712920740089674152493750849155866...
%K A153306 nonn,cons,new
%O A153306 0,1
%A A153306 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153269
%S A153269 6,7,1,1,8,7,7,4,1,4,7,1,2,3,9,6,3,8,1,3,9,9,0,0,6,3,7,3,1,8,9,9,6,8,2,
%T A153269 3,4,8,4,9,8,5,7,0,2,4,1,3,0,0,7,8,6,9,5,9,6,9,0,9,6,1,9,8,7,3,5,4,6,8,
%U A153269 6,5,6,5,1,4,8,9,0,3,1,2,1,9,9,2,7,1,1,4,6,2,8,4,1,5,7,8,0
%N A153269 Decimal expansion of log_11 (5).
%e A153269 .67118774147123963813990063731899682348498570241300786959690...
%K A153269 nonn,cons,new
%O A153269 0,1
%A A153269 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153268
%S A153268 6,9,8,9,7,0,0,0,4,3,3,6,0,1,8,8,0,4,7,8,6,2,6,1,1,0,5,2,7,5,5,0,6,9,7,
%T A153268 3,2,3,1,8,1,0,1,1,8,5,3,7,8,9,1,4,5,8,6,8,9,5,7,2,5,3,8,8,7,2,8,9,1,8,
%U A153268 1,0,7,2,5,5,7,5,4,9,0,5,1,3,0,7,2,7,4,7,8,8,1,8,1,3,8,2,7
%N A153268 Decimal expansion of log_10 (5).
%e A153268 .69897000433601880478626110527550697323181011853789145868957...
%K A153268 nonn,cons,new
%O A153268 0,1
%A A153268 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153205
%S A153205 7,3,2,4,8,6,7,6,0,3,5,8,9,6,3,5,8,3,5,9,8,5,2,0,2,0,3,8,3,9,3,2,0,1,9,
%T A153205 8,1,5,3,9,6,6,1,8,3,3,3,3,0,2,4,8,4,4,5,2,6,4,4,5,1,9,7,3,9,7,7,4,6,1,
%U A153205 3,8,0,9,5,5,1,2,9,1,1,8,2,7,7,9,6,5,5,6,8,7,9,7,6,4,7,4,5
%N A153205 Decimal expansion of log_9 (5).
%e A153205 .73248676035896358359852020383932019815396618333302484452644...
%K A153205 nonn,cons,new
%O A153205 0,1
%A A153205 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153204
%S A153204 7,7,3,9,7,6,0,3,1,6,2,9,1,2,0,7,8,2,6,2,3,4,3,9,8,0,9,8,2,9,7,9,6,7,2,
%T A153204 5,2,8,8,2,7,7,1,3,1,0,0,8,1,9,3,5,3,7,3,5,1,5,8,5,4,6,5,2,7,1,9,7,8,2,
%U A153204 5,8,8,6,9,5,4,1,7,3,8,6,1,6,7,1,3,2,4,7,7,8,6,4,5,6,7,1,8
%N A153204 Decimal expansion of log_8 (5).
%e A153204 .77397603162912078262343980982979672528827713100819353735158...
%K A153204 nonn,cons,new
%O A153204 0,1
%A A153204 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153203
%S A153203 8,2,7,0,8,7,4,7,5,3,4,6,9,1,6,1,5,0,3,0,3,7,5,1,4,8,3,6,4,5,5,6,8,6,1,
%T A153203 8,8,6,7,6,8,7,3,6,0,1,6,9,5,8,1,0,2,3,3,1,6,7,6,4,4,5,2,6,6,5,0,4,4,2,
%U A153203 9,6,1,8,9,2,0,0,7,5,7,3,0,9,6,2,4,0,9,6,2,5,2,5,0,8,4,9,7
%N A153203 Decimal expansion of log_7 (5).
%e A153203 .82708747534691615030375148364556861886768736016958102331676...
%K A153203 nonn,cons,new
%O A153203 0,1
%A A153203 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153202
%S A153202 8,9,8,2,4,4,4,0,1,7,0,3,9,2,7,1,7,3,0,7,3,2,3,2,9,5,8,0,8,6,4,6,8,6,7,
%T A153202 2,2,5,0,5,9,1,3,5,3,8,2,4,6,4,7,7,9,9,4,8,0,6,9,8,9,8,9,2,4,3,3,5,1,1,
%U A153202 7,5,0,7,6,1,3,9,6,3,0,3,1,4,6,8,0,6,9,6,7,6,6,1,6,9,4,7,7
%N A153202 Decimal expansion of log_6 (5).
%e A153202 .89824440170392717307323295808646867225059135382464779948069...
%K A153202 nonn,cons,new
%O A153202 0,1
%A A153202 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153201
%S A153201 1,1,6,0,9,6,4,0,4,7,4,4,3,6,8,1,1,7,3,9,3,5,1,5,9,7,1,4,7,4,4,6,9,5,0,
%T A153201 8,7,9,3,2,4,1,5,6,9,6,5,1,2,2,9,0,3,0,6,0,2,7,3,7,8,1,9,7,9,0,7,9,6,7,
%U A153201 3,8,8,3,0,4,3,1,2,6,0,7,9,2,5,0,6,9,8,7,1,6,7,9,6,8,5,0,7
%N A153201 Decimal expansion of log_4 (5).
%e A153201 1.1609640474436811739351597147446950879324156965122903060273...
%K A153201 nonn,cons,new
%O A153201 1,3
%A A153201 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153200
%S A153200 4,3,6,2,0,8,5,8,3,9,7,1,0,6,3,1,1,8,4,5,8,6,7,5,6,1,2,8,8,6,7,7,6,7,7,
%T A153200 7,2,5,5,3,2,0,8,5,0,9,9,8,9,9,9,5,3,5,2,2,9,4,7,6,3,1,2,9,2,8,3,6,8,4,
%U A153200 7,6,3,0,0,1,9,8,4,7,0,1,9,5,9,8,3,5,4,2,8,3,7,6,4,4,4,2,8
%N A153200 Decimal expansion of log_24 (4).
%e A153200 .43620858397106311845867561288677677725532085099899953522947...
%K A153200 nonn,cons,new
%O A153200 0,1
%A A153200 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153163
%S A153163 4,4,2,1,2,9,4,5,8,9,1,5,0,0,7,4,9,2,2,9,9,5,9,2,1,0,8,1,9,0,8,6,7,0,2,
%T A153163 9,6,9,3,4,7,8,2,0,7,3,5,3,1,1,3,3,0,8,0,5,6,1,1,8,4,6,9,3,2,9,1,1,5,6,
%U A153163 4,5,5,2,0,4,4,4,8,5,8,6,7,6,6,3,5,0,0,1,1,3,3,6,9,6,5,8,5
%N A153163 Decimal expansion of log_23 (4).
%e A153163 .44212945891500749229959210819086702969347820735311330805611...
%K A153163 nonn,cons,new
%O A153163 0,1
%A A153163 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153132
%S A153132 4,4,8,4,8,7,6,4,8,4,3,5,1,5,0,8,7,8,9,5,5,1,2,4,6,7,6,8,0,6,9,6,0,9,4,
%T A153132 1,7,9,5,8,2,5,7,6,4,8,8,4,4,4,4,0,1,9,4,5,1,5,2,3,4,2,2,1,3,0,2,2,9,0,
%U A153132 6,0,0,1,2,8,0,2,8,4,7,8,3,5,1,5,8,9,5,3,8,6,1,4,0,7,7,3,1
%N A153132 Decimal expansion of log_22 (4).
%e A153132 .44848764843515087895512467680696094179582576488444401945152...
%K A153132 nonn,cons,new
%O A153132 0,1
%A A153132 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153131
%S A153131 4,5,5,3,4,0,4,9,7,3,9,3,9,0,5,9,9,5,9,6,4,1,5,1,9,4,4,2,0,1,7,8,1,9,9,
%T A153131 1,2,8,2,1,3,1,1,8,2,4,8,2,6,4,6,5,9,2,3,3,4,1,4,9,9,1,3,4,3,1,2,1,7,3,
%U A153131 6,8,5,1,3,7,0,9,5,3,5,1,6,5,7,6,8,9,6,3,0,5,3,4,6,8,1,7,7
%N A153131 Decimal expansion of log_21 (4).
%e A153131 .45534049739390599596415194420178199128213118248264659233414...
%K A153131 nonn,cons,new
%O A153131 0,1
%A A153131 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153124
%S A153124 4,6,2,7,5,6,4,2,6,3,1,9,5,1,8,3,4,8,5,2,7,3,9,5,4,0,2,1,9,5,2,8,0,9,9,
%T A153124 1,7,8,1,9,3,1,0,1,4,7,4,7,1,3,1,7,2,3,6,7,9,2,3,5,5,8,8,2,2,7,0,4,9,1,
%U A153124 0,8,0,6,0,3,1,6,7,6,9,4,2,7,9,3,1,1,6,8,0,8,9,5,0,7,8,5,1
%N A153124 Decimal expansion of log_20 (4).
%e A153124 .46275642631951834852739540219528099178193101474713172367923...
%K A153124 nonn,cons,new
%O A153124 0,1
%A A153124 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153117
%S A153117 4,7,0,8,1,7,8,2,6,7,3,3,2,7,6,4,7,2,8,9,3,9,3,0,9,2,0,0,7,3,6,8,3,7,0,
%T A153117 7,6,7,0,8,1,3,5,5,3,2,5,5,6,3,2,0,9,4,5,7,6,2,6,4,7,3,7,0,0,5,7,1,4,6,
%U A153117 0,4,2,6,4,1,0,8,9,6,3,5,0,4,8,8,0,0,9,1,7,4,9,5,6,7,2,7,3
%N A153117 Decimal expansion of log_19 (4).
%e A153117 .47081782673327647289393092007368370767081355325563209457626...
%K A153117 nonn,cons,new
%O A153117 0,1
%A A153117 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153113
%S A153113 4,7,9,6,2,4,9,3,3,1,3,6,2,6,2,8,8,9,4,7,1,3,6,8,3,2,9,8,2,1,0,4,6,1,2,
%T A153113 3,5,3,6,3,5,5,8,6,0,0,3,8,1,4,1,1,3,1,9,5,7,2,8,9,8,0,1,4,2,9,8,2,5,8,
%U A153113 1,1,4,8,6,3,7,9,0,8,9,7,0,1,3,1,1,2,8,2,9,6,0,2,8,2,2,4,8
%N A153113 Decimal expansion of log_18 (4).
%e A153113 .47962493313626288947136832982104612353635586003814113195728...
%K A153113 nonn,cons,new
%O A153113 0,1
%A A153113 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153109
%S A153109 4,8,9,3,0,1,0,8,4,2,3,6,4,5,2,0,6,0,7,7,9,5,2,2,9,8,2,4,6,3,9,5,5,6,1,
%T A153109 4,7,8,8,5,2,1,9,3,1,2,1,6,7,2,7,3,9,5,5,7,2,7,0,0,7,8,5,0,5,4,3,9,4,6,
%U A153109 2,2,3,1,4,1,0,5,3,7,1,8,9,8,5,5,3,0,3,7,6,0,9,6,0,0,6,1,5
%N A153109 Decimal expansion of log_17 (4).
%e A153109 .48930108423645206077952298246395561478852193121672739557270...
%K A153109 nonn,cons,new
%O A153109 0,1
%A A153109 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153108
%S A153108 5,1,1,9,1,6,0,4,9,6,1,9,6,3,0,9,7,8,7,7,5,3,5,5,3,5,7,7,2,9,6,0,4,5,4,
%T A153108 0,8,0,9,8,8,3,7,5,9,5,1,7,8,0,2,2,8,4,5,3,7,0,3,0,8,6,1,8,5,9,2,3,8,4,
%U A153108 3,9,5,4,4,3,4,4,9,8,9,0,2,9,4,5,5,1,6,7,7,0,5,9,0,5,5,8,9
%N A153108 Decimal expansion of log_15 (4).
%e A153108 .51191604961963097877535535772960454080988375951780228453703...
%K A153108 nonn,cons,new
%O A153108 0,1
%A A153108 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153107
%S A153107 5,2,5,2,9,9,0,7,0,0,7,4,3,8,7,0,9,5,9,5,7,8,1,3,7,3,7,1,3,0,1,6,1,4,4,
%T A153107 1,2,0,1,3,2,3,1,8,9,4,1,3,8,3,9,6,1,9,7,8,4,0,8,5,1,3,2,2,1,5,3,9,2,0,
%U A153107 9,9,9,9,5,0,3,5,0,9,2,5,7,5,0,3,1,7,1,8,0,3,6,3,1,6,8,2,5
%N A153107 Decimal expansion of log_14 (4).
%e A153107 .52529907007438709595781373713016144120132318941383961978408...
%K A153107 nonn,cons,new
%O A153107 0,1
%A A153107 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153106
%S A153106 5,4,0,4,7,6,3,0,8,8,5,4,6,3,9,4,8,2,5,8,8,2,1,6,0,0,6,9,0,1,2,8,4,5,8,
%T A153106 8,7,9,7,2,8,8,4,0,4,6,2,7,3,6,2,2,9,8,8,0,5,5,6,4,9,6,1,3,4,7,3,5,1,3,
%U A153106 8,7,4,6,8,9,0,6,2,4,0,6,0,6,1,6,5,7,9,8,7,5,0,2,5,4,3,4,9
%N A153106 Decimal expansion of log_13 (4).
%e A153106 .54047630885463948258821600690128458879728840462736229880556...
%K A153106 nonn,cons,new
%O A153106 0,1
%A A153106 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153105
%S A153105 5,5,7,8,8,5,8,9,1,3,0,2,2,5,9,6,8,6,3,8,2,0,8,8,1,6,2,0,7,5,7,7,1,2,0,
%T A153105 6,2,0,9,5,8,8,6,7,5,1,9,2,9,4,6,1,3,5,9,4,5,3,9,2,0,0,6,8,1,6,5,5,3,0,
%U A153105 1,0,4,8,0,9,3,5,1,1,8,1,6,1,3,9,4,4,3,4,7,0,0,7,2,6,2,3,1
%N A153105 Decimal expansion of log_12 (4).
%e A153105 .55788589130225968638208816207577120620958867519294613594539...
%K A153105 nonn,cons,new
%O A153105 0,1
%A A153105 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153104
%S A153104 5,7,8,1,2,9,6,5,2,6,3,5,7,7,5,7,1,8,5,3,2,4,2,2,0,1,5,4,0,0,5,2,7,1,3,
%T A153104 2,3,8,2,5,8,9,2,3,1,9,7,1,3,9,2,0,0,7,2,5,2,6,8,3,1,3,5,5,9,7,0,6,3,1,
%U A153104 6,7,1,1,3,8,3,1,5,4,3,8,6,5,9,5,4,1,8,3,0,7,8,3,9,5,6,3,1
%N A153104 Decimal expansion of log_11 (4).
%e A153104 .57812965263577571853242201540052713238258923197139200725268...
%K A153104 nonn,cons,new
%O A153104 0,1
%A A153104 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153103
%S A153103 7,1,2,4,1,4,3,7,4,2,1,6,0,4,4,3,5,3,0,2,8,3,5,4,1,5,6,0,0,2,5,8,1,0,5,
%T A153103 8,5,9,5,5,1,4,3,2,5,5,4,5,6,2,7,4,0,0,0,7,9,1,5,2,9,1,5,5,8,1,7,3,5,1,
%U A153103 6,0,7,1,8,5,1,8,6,8,9,3,2,7,7,4,8,1,3,1,0,9,9,5,4,5,7,2,2
%N A153103 Decimal expansion of log_7 (4).
%e A153103 .71241437421604435302835415600258105859551432554562740007915...
%K A153103 nonn,cons,new
%O A153103 0,1
%A A153103 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153102
%S A153102 7,7,3,7,0,5,6,1,4,4,6,9,0,8,3,1,7,3,7,4,0,4,9,2,2,7,6,9,3,5,6,4,1,7,5,
%T A153102 2,9,3,0,2,8,3,7,1,8,9,1,4,2,0,6,8,5,6,7,7,8,9,8,9,8,5,7,6,5,3,2,8,4,0,
%U A153102 3,7,0,8,1,4,4,5,6,0,7,6,6,3,3,0,4,6,0,0,5,8,9,6,3,2,0,0,9
%N A153102 Decimal expansion of log_6 (4).
%e A153102 .77370561446908317374049227693564175293028371891420685677898...
%K A153102 nonn,cons,new
%O A153102 0,1
%A A153102 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153101
%S A153101 8,6,1,3,5,3,1,1,6,1,4,6,7,8,6,1,0,1,3,4,0,2,1,3,1,3,7,5,2,7,9,3,1,2,6,
%T A153101 4,1,3,9,5,8,3,8,6,4,1,5,9,5,2,0,8,9,8,6,4,3,9,5,2,0,7,5,9,2,1,3,2,4,1,
%U A153101 6,5,0,7,5,7,7,1,0,1,2,1,6,7,3,9,6,1,9,8,8,9,0,5,3,3,9,5,1
%N A153101 Decimal expansion of log_5 (4).
%e A153101 .86135311614678610134021313752793126413958386415952089864395...
%K A153101 nonn,cons,new
%O A153101 0,1
%A A153101 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153100
%S A153100 3,4,5,6,8,7,1,2,4,0,4,3,4,0,5,3,2,2,3,1,1,9,8,6,5,8,0,6,6,9,8,3,4,8,3,
%T A153100 4,1,1,7,0,1,8,7,2,3,5,0,1,5,0,0,6,9,7,1,5,5,7,8,5,5,3,0,6,0,7,4,4,7,2,
%U A153100 8,5,5,4,9,7,0,2,2,9,4,7,0,6,0,2,4,6,8,5,7,4,3,5,3,3,3,5,7
%N A153100 Decimal expansion of log_24 (3).
%e A153100 .34568712404340532231198658066983483411701872350150069715578...
%K A153100 nonn,cons,new
%O A153100 0,1
%A A153100 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153099
%S A153099 3,5,0,3,7,9,3,0,6,4,2,2,2,1,0,9,7,7,4,0,6,6,2,3,4,0,8,6,4,3,9,7,1,4,3,
%T A153099 1,8,5,6,4,9,9,8,5,2,5,1,5,1,3,8,3,4,1,9,9,4,1,2,5,6,6,9,6,3,5,1,1,8,8,
%U A153099 0,8,8,5,6,1,7,6,9,0,8,7,1,9,4,7,8,2,6,9,9,0,6,9,4,4,6,3,6
%N A153099 Decimal expansion of log_23 (3).
%e A153099 .35037930642221097740662340864397143185649985251513834199412...
%K A153099 nonn,cons,new
%O A153099 0,1
%A A153099 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153098
%S A153098 3,5,5,4,1,8,0,5,2,4,0,3,1,6,3,7,3,2,4,8,0,2,8,6,0,7,0,7,8,2,1,6,4,3,8,
%T A153098 7,5,2,0,1,7,8,3,4,1,8,3,1,2,1,6,7,3,6,3,0,6,2,1,3,2,2,7,8,9,0,6,5,8,7,
%U A153098 1,8,0,3,2,0,9,3,1,1,1,3,7,5,6,0,5,6,9,1,7,5,5,1,1,4,6,3,4
%N A153098 Decimal expansion of log_22 (3).
%e A153098 .35541805240316373248028607078216438752017834183121673630621...
%K A153098 nonn,cons,new
%O A153098 0,1
%A A153098 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153097
%S A153097 3,6,0,8,4,8,8,0,6,7,1,4,5,3,0,1,7,3,2,4,5,0,8,3,7,9,6,5,0,4,3,0,5,2,6,
%T A153097 0,0,6,4,3,8,6,4,7,9,7,4,8,7,5,7,6,4,7,6,5,9,5,8,8,1,3,7,0,6,1,4,6,9,9,
%U A153097 4,8,1,8,1,2,7,5,9,7,8,9,0,0,3,9,3,0,8,8,8,6,7,0,9,3,2,5,1
%N A153097 Decimal expansion of log_21 (3).
%e A153097 .36084880671453017324508379650430526006438647974875764765958...
%K A153097 nonn,cons,new
%O A153097 0,1
%A A153097 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153035
%S A153035 3,6,6,7,2,5,7,9,1,3,4,2,0,8,4,6,2,8,9,1,2,8,0,7,1,4,2,6,5,9,3,3,2,6,5,
%T A153035 3,5,9,5,7,6,8,4,3,0,9,3,2,3,3,2,0,6,8,2,8,8,9,8,7,5,7,7,2,7,4,9,4,6,6,
%U A153035 9,6,9,3,1,5,6,9,1,0,9,3,7,8,8,0,5,9,3,7,7,8,4,4,0,6,4,1,5
%N A153035 Decimal expansion of log_20 (3).
%e A153035 .36672579134208462891280714265933265359576843093233206828898...
%K A153035 nonn,cons,new
%O A153035 0,1
%A A153035 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153027
%S A153027 3,7,3,1,1,4,3,0,0,0,2,1,6,3,6,9,4,8,8,7,8,2,3,2,3,6,8,1,0,5,1,9,3,0,3,
%T A153027 6,2,2,5,6,1,6,7,4,8,2,5,2,1,3,6,3,5,7,9,8,8,8,6,6,2,4,1,9,4,6,8,8,0,1,
%U A153027 9,1,7,2,3,0,4,7,3,1,7,0,2,4,0,3,0,0,4,9,9,1,6,6,9,0,1,7,0
%N A153027 Decimal expansion of log_19 (3).
%e A153027 .37311430002163694887823236810519303622561674825213635798886...
%K A153027 nonn,cons,new
%O A153027 0,1
%A A153027 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153021
%S A153021 3,8,0,0,9,3,7,6,6,7,1,5,9,3,4,2,7,7,6,3,2,1,5,7,9,1,7,5,4,4,7,3,8,4,6,
%T A153021 9,1,1,5,9,1,1,0,3,4,9,9,0,4,6,4,7,1,7,0,1,0,6,7,7,5,4,9,6,4,2,5,4,3,5,
%U A153021 4,7,1,2,8,4,0,5,2,2,7,5,7,4,6,7,2,1,7,9,2,5,9,9,2,9,4,3,7
%N A153021 Decimal expansion of log_18 (3).
%e A153021 .38009376671593427763215791754473846911591103499046471701067...
%K A153021 nonn,cons,new
%O A153021 0,1
%A A153021 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153020
%S A153020 3,8,7,7,6,1,9,3,5,0,3,8,4,9,0,0,7,5,4,3,6,1,9,9,3,6,0,7,3,4,4,1,8,6,4,
%T A153020 6,8,3,0,6,7,3,6,2,9,4,4,3,8,7,6,2,4,2,3,4,6,7,5,8,2,1,5,2,9,0,8,0,9,3,
%U A153020 1,2,7,9,3,3,5,3,0,5,7,0,5,4,3,9,0,8,2,7,1,9,7,8,8,1,4,1,5
%N A153020 Decimal expansion of log_17 (3).
%e A153020 .38776193503849007543619936073441864683067362944387624234675...
%K A153020 nonn,cons,new
%O A153020 0,1
%A A153020 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153019
%S A153019 3,9,6,2,4,0,6,2,5,1,8,0,2,8,9,0,4,5,3,6,3,4,3,4,7,3,5,9,8,6,9,5,4,1,2,
%T A153019 7,1,8,9,9,5,3,6,0,1,9,2,3,1,2,0,2,6,5,1,1,3,9,3,8,1,6,3,6,3,5,2,7,4,5,
%U A153019 5,6,9,4,8,5,8,9,6,4,0,6,3,0,5,7,0,1,1,8,7,2,9,5,2,2,0,6,0
%N A153019 Decimal expansion of log_16 (3).
%e A153019 .39624062518028904536343473598695412718995360192312026511393...
%K A153019 nonn,cons,new
%O A153019 0,1
%A A153019 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153018
%S A153018 4,0,5,6,8,3,8,7,1,0,8,2,2,1,2,8,9,4,3,8,2,9,0,4,9,9,6,6,0,1,3,9,2,5,2,
%T A153018 9,4,9,9,8,6,7,7,7,8,2,6,6,2,8,0,4,2,7,4,2,6,3,4,7,0,2,6,1,8,1,1,7,1,1,
%U A153018 7,3,2,8,9,0,7,2,7,9,6,3,8,0,6,1,4,7,9,1,1,1,3,5,5,4,2,5,8
%N A153018 Decimal expansion of log_15 (3).
%e A153018 .40568387108221289438290499660139252949986777826628042742634...
%K A153018 nonn,cons,new
%O A153018 0,1
%A A153018 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153017
%S A153017 4,1,6,2,8,9,6,6,3,8,6,5,7,9,9,2,1,4,5,3,6,5,4,0,6,9,2,3,4,2,5,5,1,7,2,
%T A153017 8,9,8,6,7,9,8,9,9,3,7,2,4,4,1,5,9,1,6,7,4,6,4,0,6,2,3,7,6,6,4,0,9,9,7,
%U A153017 4,5,1,7,7,1,0,9,8,8,3,8,9,8,2,3,8,5,8,9,0,0,1,6,9,5,4,0,8
%N A153017 Decimal expansion of log_14 (3).
%e A153017 .41628966386579921453654069234255172898679899372441591674640...
%K A153017 nonn,cons,new
%O A153017 0,1
%A A153017 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153016
%S A153016 4,2,8,3,1,7,3,4,1,0,3,1,3,9,4,6,8,0,9,9,0,7,7,4,3,7,7,9,2,0,9,6,4,5,7,
%T A153016 6,9,0,6,6,3,0,9,2,8,3,8,3,6,8,4,6,1,6,9,9,9,8,2,0,5,6,8,9,8,9,2,8,2,1,
%U A153016 2,2,5,2,3,4,0,3,5,3,7,1,9,8,7,3,6,5,1,8,8,1,3,6,7,5,7,8,0
%N A153016 Decimal expansion of log_13 (3).
%e A153016 .42831734103139468099077437792096457690663092838368461699982...
%K A153016 nonn,cons,new
%O A153016 0,1
%A A153016 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A153015
%S A153015 4,4,2,1,1,4,1,0,8,6,9,7,7,4,0,3,1,3,6,1,7,9,1,1,8,3,7,9,2,4,2,2,8,7,9,
%T A153015 3,7,9,0,4,1,1,3,2,4,8,0,7,0,5,3,8,6,4,0,5,4,6,0,7,9,9,3,1,8,3,4,4,6,9,
%U A153015 8,9,5,1,9,0,6,4,8,8,1,8,3,8,6,0,5,5,6,5,2,9,9,2,7,3,7,6,8
%N A153015 Decimal expansion of log_12 (3).
%e A153015 .44211410869774031361791183792422879379041132480705386405460...
%K A153015 nonn,cons,new
%O A153015 0,1
%A A153015 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A152974
%S A152974 4,5,8,1,5,6,9,0,9,9,9,1,3,2,6,2,2,2,4,8,2,2,1,8,2,3,3,8,9,2,7,5,2,6,1,
%T A152974 8,9,2,4,6,1,9,3,8,5,6,2,4,8,1,7,3,2,8,6,6,2,3,1,9,4,7,2,2,2,7,2,9,8,8,
%U A152974 0,2,6,2,4,5,1,1,2,6,4,4,4,4,4,5,6,0,4,8,4,8,4,5,8,5,5,1,3
%N A152974 Decimal expansion of log_11 (3).
%e A152974 .45815690999132622248221823389275261892461938562481732866231...
%K A152974 nonn,cons,new
%O A152974 0,1
%A A152974 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A152956
%S A152956 5,2,8,3,2,0,8,3,3,5,7,3,7,1,8,7,2,7,1,5,1,2,4,6,3,1,4,6,4,9,2,7,2,1,6,
%T A152956 9,5,8,6,6,0,4,8,0,2,5,6,4,1,6,0,3,5,3,4,8,5,2,5,0,8,8,4,8,4,7,0,3,2,7,
%U A152956 4,2,5,9,8,1,1,9,5,2,0,8,4,0,7,6,0,1,5,8,3,0,6,0,2,9,4,1,4
%N A152956 Decimal expansion of log_8 (3).
%e A152956 .52832083357371872715124631464927216958660480256416035348525...
%K A152956 nonn,cons,new
%O A152956 0,1
%A A152956 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A152945
%S A152945 5,6,4,5,7,5,0,3,4,0,5,3,5,7,9,6,1,3,8,0,4,5,5,0,1,6,7,1,7,4,9,0,8,5,3,
%T A152945 6,1,4,3,2,2,7,9,1,1,1,8,6,7,9,2,5,9,5,0,4,5,4,0,9,2,6,2,3,0,7,7,5,2,3,
%U A152945 1,4,2,0,0,4,0,9,4,9,9,0,1,0,2,8,1,5,4,4,5,8,4,3,6,1,2,6,0
%N A152945 Decimal expansion of log_7 (3).
%e A152945 .56457503405357961380455016717490853614322791118679259504540...
%K A152945 nonn,cons,new
%O A152945 0,1
%A A152945 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A152935
%S A152935 6,1,3,1,4,7,1,9,2,7,6,5,4,5,8,4,1,3,1,2,9,7,5,3,8,6,1,5,3,2,1,7,9,1,2,
%T A152935 3,5,3,4,8,5,8,1,4,0,5,4,2,8,9,6,5,7,1,6,1,0,5,0,5,0,7,1,1,7,3,3,5,7,9,
%U A152935 8,1,4,5,9,2,7,7,1,9,6,1,6,8,3,4,7,6,9,9,7,0,5,1,8,3,9,9,5
%N A152935 Decimal expansion of log_6 (3).
%e A152935 .61314719276545841312975386153217912353485814054289657161050...
%K A152935 nonn,cons,new
%O A152935 0,1
%A A152935 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A152914
%S A152914 6,8,2,6,0,6,1,9,4,4,8,5,9,8,5,2,9,5,1,3,4,5,6,6,3,5,9,2,7,1,0,5,2,2,5,
%T A152914 3,0,2,4,6,6,9,3,9,9,8,7,3,1,6,7,2,0,9,6,6,0,0,5,6,6,9,1,4,9,3,7,4,6,1,
%U A152914 6,2,9,2,6,9,1,3,2,7,7,3,3,6,9,5,4,2,2,0,9,2,2,3,2,0,2,4,0
%N A152914 Decimal expansion of log_5 (3).
%e A152914 .68260619448598529513456635927105225302466939987316720966005...
%K A152914 nonn,cons,new
%O A152914 0,1
%A A152914 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A152901
%S A152901 2,1,8,1,0,4,2,9,1,9,8,5,5,3,1,5,5,9,2,2,9,3,3,7,8,0,6,4,4,3,3,8,8,3,8,
%T A152901 8,6,2,7,6,6,0,4,2,5,4,9,9,4,9,9,7,6,7,6,1,4,7,3,8,1,5,6,4,6,4,1,8,4,2,
%U A152901 3,8,1,5,0,0,9,9,2,3,5,0,9,7,9,9,1,7,7,1,4,1,8,8,2,2,2,1,4
%N A152901 Decimal expansion of log_24 (2).
%e A152901 .21810429198553155922933780644338838862766042549949976761473...
%K A152901 nonn,cons,new
%O A152901 0,1
%A A152901 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A152882
%S A152882 2,2,1,0,6,4,7,2,9,4,5,7,5,0,3,7,4,6,1,4,9,7,9,6,0,5,4,0,9,5,4,3,3,5,1,
%T A152882 4,8,4,6,7,3,9,1,0,3,6,7,6,5,5,6,6,5,4,0,2,8,0,5,9,2,3,4,6,6,4,5,5,7,8,
%U A152882 2,2,7,6,0,2,2,2,4,2,9,3,3,8,3,1,7,5,0,0,5,6,6,8,4,8,2,9,2
%N A152882 Decimal expansion of log_23 (2).
%e A152882 .22106472945750374614979605409543351484673910367655665402805...
%K A152882 nonn,cons,new
%O A152882 0,1
%A A152882 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A152858
%S A152858 2,2,4,2,4,3,8,2,4,2,1,7,5,7,5,4,3,9,4,7,7,5,6,2,3,3,8,4,0,3,4,8,0,4,7,
%T A152858 0,8,9,7,9,1,2,8,8,2,4,4,2,2,2,2,0,0,9,7,2,5,7,6,1,7,1,1,0,6,5,1,1,4,5,
%U A152858 3,0,0,0,6,4,0,1,4,2,3,9,1,7,5,7,9,4,7,6,9,3,0,7,0,3,8,6,5
%N A152858 Decimal expansion of log_22 (2).
%e A152858 .22424382421757543947756233840348047089791288244222200972576...
%K A152858 nonn,cons,new
%O A152858 0,1
%A A152858 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A152825
%S A152825 2,2,7,6,7,0,2,4,8,6,9,6,9,5,2,9,9,7,9,8,2,0,7,5,9,7,2,1,0,0,8,9,0,9,9,
%T A152825 5,6,4,1,0,6,5,5,9,1,2,4,1,3,2,3,2,9,6,1,6,7,0,7,4,9,5,6,7,1,5,6,0,8,6,
%U A152825 8,4,2,5,6,8,5,4,7,6,7,5,8,2,8,8,4,4,8,1,5,2,6,7,3,4,0,8,8
%N A152825 Decimal expansion of log_21 (2).
%e A152825 .22767024869695299798207597210089099564106559124132329616707...
%K A152825 nonn,cons,new
%O A152825 0,1
%A A152825 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A152821
%S A152821 2,3,1,3,7,8,2,1,3,1,5,9,7,5,9,1,7,4,2,6,3,6,9,7,7,0,1,0,9,7,6,4,0,4,9,
%T A152821 5,8,9,0,9,6,5,5,0,7,3,7,3,5,6,5,8,6,1,8,3,9,6,1,7,7,9,4,1,1,3,5,2,4,5,
%U A152821 5,4,0,3,0,1,5,8,3,8,4,7,1,3,9,6,5,5,8,4,0,4,4,7,5,3,9,2,5
%N A152821 Decimal expansion of log_20 (2).
%e A152821 .23137821315975917426369770109764049589096550737356586183961...
%K A152821 nonn,cons,new
%O A152821 0,1
%A A152821 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A152814
%S A152814 2,3,5,4,0,8,9,1,3,3,6,6,6,3,8,2,3,6,4,4,6,9,6,5,4,6,0,0,3,6,8,4,1,8,5,
%T A152814 3,8,3,5,4,0,6,7,7,6,6,2,7,8,1,6,0,4,7,2,8,8,1,3,2,3,6,8,5,0,2,8,5,7,3,
%U A152814 0,2,1,3,2,0,5,4,4,8,1,7,5,2,4,4,0,0,4,5,8,7,4,7,8,3,6,3,6
%N A152814 Decimal expansion of log_19 (2).
%e A152814 .23540891336663823644696546003684185383540677662781604728813...
%K A152814 nonn,cons,new
%O A152814 0,1
%A A152814 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A152812
%S A152812 2,3,9,8,1,2,4,6,6,5,6,8,1,3,1,4,4,4,7,3,5,6,8,4,1,6,4,9,1,0,5,2,3,0,6,
%T A152812 1,7,6,8,1,7,7,9,3,0,0,1,9,0,7,0,5,6,5,9,7,8,6,4,4,9,0,0,7,1,4,9,1,2,9,
%U A152812 0,5,7,4,3,1,8,9,5,4,4,8,5,0,6,5,5,6,4,1,4,8,0,1,4,1,1,2,4
%N A152812 Decimal expansion of log_18 (2).
%e A152812 .23981246656813144473568416491052306176817793001907056597864...
%K A152812 nonn,cons,new
%O A152812 0,1
%A A152812 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A152782
%S A152782 2,4,4,6,5,0,5,4,2,1,1,8,2,2,6,0,3,0,3,8,9,7,6,1,4,9,1,2,3,1,9,7,7,8,0,
%T A152782 7,3,9,4,2,6,0,9,6,5,6,0,8,3,6,3,6,9,7,7,8,6,3,5,0,3,9,2,5,2,7,1,9,7,3,
%U A152782 1,1,1,5,7,0,5,2,6,8,5,9,4,9,2,7,6,5,1,8,8,0,4,8,0,0,3,0,7
%N A152782 Decimal expansion of log_17 (2).
%e A152782 .24465054211822603038976149123197780739426096560836369778635...
%K A152782 nonn,cons,new
%O A152782 0,1
%A A152782 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A152781
%S A152781 2,5,5,9,5,8,0,2,4,8,0,9,8,1,5,4,8,9,3,8,7,6,7,7,6,7,8,8,6,4,8,0,2,2,7,
%T A152781 0,4,0,4,9,4,1,8,7,9,7,5,8,9,0,1,1,4,2,2,6,8,5,1,5,4,3,0,9,2,9,6,1,9,2,
%U A152781 1,9,7,7,2,1,7,2,4,9,4,5,1,4,7,2,7,5,8,3,8,5,2,9,5,2,7,9,4
%N A152781 Decimal expansion of log_15 (2).
%e A152781 .25595802480981548938767767886480227040494187975890114226851...
%K A152781 nonn,cons,new
%O A152781 0,1
%A A152781 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A152780
%S A152780 2,6,2,6,4,9,5,3,5,0,3,7,1,9,3,5,4,7,9,7,8,9,0,6,8,6,8,5,6,5,0,8,0,7,2,
%T A152780 0,6,0,0,6,6,1,5,9,4,7,0,6,9,1,9,8,0,9,8,9,2,0,4,2,5,6,6,1,0,7,6,9,6,0,
%U A152780 4,9,9,9,7,5,1,7,5,4,6,2,8,7,5,1,5,8,5,9,0,1,8,1,5,8,4,1,2
%N A152780 Decimal expansion of log_14 (2).
%e A152780 .26264953503719354797890686856508072060066159470691980989204...
%K A152780 nonn,cons,new
%O A152780 0,1
%A A152780 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A152779
%S A152779 2,7,0,2,3,8,1,5,4,4,2,7,3,1,9,7,4,1,2,9,4,1,0,8,0,0,3,4,5,0,6,4,2,2,9,
%T A152779 4,3,9,8,6,4,4,2,0,2,3,1,3,6,8,1,1,4,9,4,0,2,7,8,2,4,8,0,6,7,3,6,7,5,6,
%U A152779 9,3,7,3,4,4,5,3,1,2,0,3,0,3,0,8,2,8,9,9,3,7,5,1,2,7,1,7,4
%N A152779 Decimal expansion of log_13 (2).
%e A152779 .27023815442731974129410800345064229439864420231368114940278...
%K A152779 nonn,cons,new
%O A152779 0,1
%A A152779 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A152778
%S A152778 2,7,8,9,4,2,9,4,5,6,5,1,1,2,9,8,4,3,1,9,1,0,4,4,0,8,1,0,3,7,8,8,5,6,0,
%T A152778 3,1,0,4,7,9,4,3,3,7,5,9,6,4,7,3,0,6,7,9,7,2,6,9,6,0,0,3,4,0,8,2,7,6,5,
%U A152778 0,5,2,4,0,4,6,7,5,5,9,0,8,0,6,9,7,2,1,7,3,5,0,3,6,3,1,1,5
%N A152778 Decimal expansion of log_12 (2).
%e A152778 .27894294565112984319104408103788560310479433759647306797269...
%K A152778 nonn,cons,new
%O A152778 0,1
%A A152778 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A152748
%S A152748 2,8,9,0,6,4,8,2,6,3,1,7,8,8,7,8,5,9,2,6,6,2,1,1,0,0,7,7,0,0,2,6,3,5,6,
%T A152748 6,1,9,1,2,9,4,6,1,5,9,8,5,6,9,6,0,0,3,6,2,6,3,4,1,5,6,7,7,9,8,5,3,1,5,
%U A152748 8,3,5,5,6,9,1,5,7,7,1,9,3,2,9,7,7,0,9,1,5,3,9,1,9,7,8,1,5
%N A152748 Decimal expansion of log_11 (2).
%e A152748 .28906482631788785926621100770026356619129461598569600362634...
%K A152748 nonn,cons,new
%O A152748 0,1
%A A152748 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A152747
%S A152747 3,1,5,4,6,4,8,7,6,7,8,5,7,2,8,7,1,8,5,4,9,7,6,3,5,5,7,1,7,1,3,8,0,4,2,
%T A152747 7,1,4,9,7,9,2,8,2,0,0,6,5,9,4,0,2,1,3,9,3,5,3,2,7,4,7,1,9,1,9,3,4,2,6,
%U A152747 0,0,6,9,0,4,5,7,4,0,2,5,3,0,5,8,6,3,4,4,2,7,4,7,2,5,8,7,2
%N A152747 Decimal expansion of log_9 (2).
%e A152747 .31546487678572871854976355717138042714979282006594021393532...
%K A152747 nonn,cons,new
%O A152747 0,1
%A A152747 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A152713
%S A152713 3,5,6,2,0,7,1,8,7,1,0,8,0,2,2,1,7,6,5,1,4,1,7,7,0,7,8,0,0,1,2,9,0,5,2,
%T A152713 9,2,9,7,7,5,7,1,6,2,7,7,2,8,1,3,7,0,0,0,3,9,5,7,6,4,5,7,7,9,0,8,6,7,5,
%U A152713 8,0,3,5,9,2,5,9,3,4,4,6,6,3,8,7,4,0,6,5,5,4,9,7,7,2,8,6,1
%N A152713 Decimal expansion of log_7 (2).
%e A152713 .35620718710802217651417707800129052929775716277281370003957...
%K A152713 nonn,cons,new
%O A152713 0,1
%A A152713 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A152683
%S A152683 3,8,6,8,5,2,8,0,7,2,3,4,5,4,1,5,8,6,8,7,0,2,4,6,1,3,8,4,6,7,8,2,0,8,7,
%T A152683 6,4,6,5,1,4,1,8,5,9,4,5,7,1,0,3,4,2,8,3,8,9,4,9,4,9,2,8,8,2,6,6,4,2,0,
%U A152683 1,8,5,4,0,7,2,2,8,0,3,8,3,1,6,5,2,3,0,0,2,9,4,8,1,6,0,0,4
%N A152683 Decimal expansion of log_6 (2).
%e A152683 .38685280723454158687024613846782087646514185945710342838949...
%K A152683 nonn,cons,new
%O A152683 0,1
%A A152683 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A152675
%S A152675 4,3,0,6,7,6,5,5,8,0,7,3,3,9,3,0,5,0,6,7,0,1,0,6,5,6,8,7,6,3,9,6,5,6,3,
%T A152675 2,0,6,9,7,9,1,9,3,2,0,7,9,7,6,0,4,4,9,3,2,1,9,7,6,0,3,7,9,6,0,6,6,2,0,
%U A152675 8,2,5,3,7,8,8,5,5,0,6,0,8,3,6,9,8,0,9,9,4,4,5,2,6,6,9,7,5
%N A152675 Decimal expansion of log_5 (2).
%e A152675 .43067655807339305067010656876396563206979193207976044932197...
%K A152675 nonn,cons,new
%O A152675 0,1
%A A152675 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A152627
%S A152627 7,5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T A152627 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U A152627 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N A152627 Decimal expansion of 3/4.
%e A152627 .75000000000000000000000000000000000000000000000000000000000...
%K A152627 nonn,cons,new
%O A152627 0,1
%A A152627 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A152624
%S A152624 3,5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T A152624 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U A152624 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N A152624 Decimal expansion of 7/2.
%e A152624 3.5000000000000000000000000000000000000000000000000000000000...
%K A152624 nonn,cons,new
%O A152624 1,1
%A A152624 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A152623
%S A152623 1,5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T A152623 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U A152623 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N A152623 Decimal expansion of 3/2.
%e A152623 1.5000000000000000000000000000000000000000000000000000000000...
%K A152623 nonn,cons,new
%O A152623 1,2
%A A152623 N. J. A. Sloane (njas(AT)research.att.com), Oct 30 2009

%I A066535
%S A066535 1,2,4,8,24,112,544,2368,9328,34802,129064,491768,1938336,7801744,
%T A066535 31553344,127083328,509145568,2035437440,8148505828,32728127192,
%U A066535 131880275664,532597541344,2153312518240,8710505815360,35250721087168
%N A066535 Number of ways of writing n as a sum of n squares.
%F A066535 a(n) equals the coefficient of x^n in the n-th power of Jacobi theta_3(x) where theta_3(x) = 1 + 2*Sum_{n>=1} x^(n^2). [Paul D. Hanna (pauldhanna(AT)juno.com), Oct 25 2009]
%e A066535 There are a(3)=8 solutions (x,y,z) of 3=x^2+y^2+z^2: (1,1,1), (-1,-1, -1), 3 permutations of (1,1,-1) and 3 permutations of (1,-1,-1).
%t A066535 a[ n_ ] := SumOfSquaresR[ n, n ] (* First load package NumberTheory`NumberTheoryFunctions` *)
%o A066535 (PARI) {a(n)=local(THETA3=1+2*sum(k=1,sqrtint(n),x^(k^2))+x*O(x^n));polcoeff(THETA3^n, n)} /* Paul D. Hanna (pauldhanna(AT)juno.com), Oct 25 2009 */
%Y A066535 Cf. A004018, A005875, A000118, A066536.
%Y A066535 Cf. A122141, A166952 [Paul D. Hanna (pauldhanna(AT)juno.com), Oct 25 2009]
%K A066535 nonn,new
%O A066535 0,2
%A A066535 Peter Bertok (peter(AT)bertok.com), Jan 07 2002
%E A066535 Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Jan 12, 2002.
%E A066535 a(0) added by Paul D. Hanna (pauldhanna(AT)juno.com), Oct 25 2009
%E A066535 Edited by R. J. Mathar, Oct 29 2009

%I A066536
%S A066536 1,4,12,32,90,312,1288,5504,22608,88660,339064,1297056,5043376,19975256,
%T A066536 80027280,321692928,1291650786,5177295432,20748447108,83279292960,
%U A066536 335056780464,1351064867328,5456890474248,22063059606912
%N A066536 Number of ways of writing n as a sum of n+1 squares.
%F A066536 a(n) equals the coefficient of x^n in the (n+1)-th power of Jacobi theta_3(x) where theta_3(x) = 1 + 2*Sum_{n>=1} x^(n^2). [Paul D. Hanna (pauldhanna(AT)juno.com), Oct 26 2009]
%F A066536 a(n) is divisible by n+1: a(n)/(n+1) = A166952(n) for n>=0. [Paul D. Hanna (pauldhanna(AT)juno.com), Oct 26 2009]
%e A066536 There are a(2)=12 solutions (x,y,z) of 2=x^2+y^2+z^2: 3 permutations of (1,1,0), 3 permutations of (-1,-1,0) and 6 permutations of (1, -1,0).
%t A066536 a[ n_ ] := SumOfSquaresR[ n+1, n ] (* First load package NumberTheory`NumberTheoryFunctions` *)
%o A066536 (PARI) {a(n)=local(THETA3=1+2*sum(k=1,sqrtint(n),x^(k^2))+x*O(x^n));polcoeff(THETA3^(n+1), n)} /* Paul D. Hanna (pauldhanna(AT)juno.com), Oct 26 2009*/
%Y A066536 Cf. A004018, A005875, A000118, A066535.
%Y A066536 Cf. A122141, A166952 [Paul D. Hanna (pauldhanna(AT)juno.com), Oct 26 2009]
%K A066536 nonn,new
%O A066536 0,2
%A A066536 Peter Bertok (peter(AT)bertok.com), Jan 07 2002
%E A066536 Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Jan 12, 2002
%E A066536 a(0) added by Paul D. Hanna (pauldhanna(AT)juno.com), Oct 26 2009
%E A066536 Edited by R. J. Mathar, Oct 29 2009

%I A073637
%S A073637 8,9,8,1,8,1,8,1,8,8,1,1,8,1,8,8,8,1,1,8,1,1,8,8,1,8,1,8,1,8,1,8,8,1,8,
%T A073637 1,1,1,8,8,8,1,8,1,8,1,1,1,8,1,8,8,1,8,8,8,8,1,1,8,1,8,1,8,1,8,1,1,8,1,
%U A073637 8,8,1,1,1,8,8,1,8,1,8,1,8,1,1,8,8,1,8,1,8,8,1,8,1,8,8,8,1,1
%N A073637 Digital root (cf. A010888) of prime(n)^3.
%C A073637 Apart from a(2)=9 all other terms are either 1 or 8.
%e A073637 a(3)=8 because p(3)=5 and 5^3=125 -> sum-of-digits = 8. a(4)=1 because p(3)=7 and 7^3=343 -> sum-of-digits = 10 -> sum-of-digits = 1.
%t A073637 n=3; su[x_] := Sum[IntegerDigits[x][[i]], {i, Length[IntegerDigits[x]]}]; Table[su[su[su[su[Prime[x]^n]]]], {x, 100}]
%t A073637 Table[If[(m9=Mod[Prime[n]^3,9])==0,9,m9],{n,200}]
%Y A073637 Cf. A010888, A021596, A056992, A010888, A038194, A166923.
%K A073637 nonn,base,new
%O A073637 1,1
%A A073637 Zak Seidov (zakseidov(AT)yahoo.com), Sep 01 2002, Oct 23 2009
%E A073637 Edited by njas, Oct 29 2009

%I A107798
%S A107798 2,3,5,7,11,23,47,59,61,73,89,101,223,449,557,601,823,947,1051,2333,
%T A107798 4447,5009,6113,7247,8009,11113,22247,50069,81131,222247,500009,611111,
%U A107798 722237,800089,1111151,2222243,6000679,8111581,22222223,40000409,51111161,72222823,90000049,111116561,222222227,300000089,411111461
%N A107798 Primes whose digits do not appear in two previous terms.
%C A107798 The slowest increasing sequence of primes such that a(n) shares no digit with a(n-1) and a(n-2).
%C A107798 Sequence seems to be infinite.
%C A107798 Corresponding indices of primes are in A107799. Cf. A030284 = Primes whose digits do not appear in previous term.
%t A107798 d=2;e=3;b={2, 3};id[t_]:=IntegerDigits[t];Do[p=Prime[n];If[Intersection[Union[id[d], id[e]], id[p]]=={}, b=Append[b, p];d=e;e=p], {n, 100000}];b
%Y A107798 Cf. A030284, A107799.
%K A107798 base,nonn,new
%O A107798 1,1
%A A107798 Zak Seidov (zakseidov(AT)yahoo.com), May 24 2005, Oct 23 2009
%E A107798 Edited by njas, Oct 29 2009

%I A167182
%S A167182 2,4,8,64,4096,16777216,281474976710656,79228162514264337593543950336
%N A167182 a(n) = a(n)=2^sum_{i=1..n-1} = product_{i=1..n-1} a(1) = 2 a(2) = 4.
%F A167182 a(n) = (a(n-1))^2 for n>2.
%Y A167182 Cf. A165426
%K A167182 nonn,new
%O A167182 1,1
%A A167182 Giovanni Teofilatto (g.teofilatto(AT)tiscalinet.it), Oct 29 2009

%I A167181
%S A167181 1,3,7,11,19,21,23,31,33,43,47,57,59,67,69,71,77,79,83,93,103,107,127,129,
%T A167181 131,133,139,141,151,161,163,167,177,179,191,199,201,209,211,213,217,
%U A167181 223,227,231,237,239,249,251,253,263,271,283,301,307,309,311,321,329
%N A167181 Numbers n with property that all prime factors are == 3 mod 4.
%C A167181 Or, numbers that are not divisible by the sum of two squares
%K A167181 nonn,new
%O A167181 1,2
%A A167181 Arnaud Vernier (arnaud.vernier(AT)ecl2008.ec-lyon.fr), Oct 29 2009
%E A167181 Edited by Zak Seidov, Oct 30 2009

%I A167179
%S A167179 4,6,8,10,12,15,20,25,30,35,40,45,55,60,65,70,75,80,85,90,95,100,105,
%T A167179 110,115,120,125,130,135,140,145,150,155,160,165,170,175,180,185,190,
%U A167179 195,200,205,210,215,220,225,230,235,240,245,250,255,260,265,270,275
%N A167179 The number of additional armies one receives in Parker Brothers' (now part of Hasbro) game of Risk for turning in the nth set of three different or alike cards.
%C A167179 Although this sequence is theoretically infinite, in actual practice, terms greater than a(15) are rarely reached.
%H A167179 <a href="http://en.wikipedia.org/wiki/Risk_%28game%29#Turning_in_Risk_cards"></a>
%H A167179 <a href="http://www.hasbro.com/common/instruct/risk.pdf"> rules of Risk</a>
%F A167179 a(n)=2*(n+1) for values of n less than 6,a(n)=5*(n-3) for values of n greater than 5
%K A167179 nonn,new
%O A167179 1,1
%A A167179 Michael Turniansky (mturniansky(AT)gmail.com), Oct 29 2009
%E A167179 Removed term a(5) from the %C field, and changed "n less than 5" to "n less than 6", because I'm an idiot-- the first 5 terms are regular, not just the first 4 Michael Turniansky (mturniansky(AT)gmail.com), Oct 30 2009

%I A167178
%S A167178 10,11,12,103,54,45,256,1007,258,1009,110,10011,2512,10013,2514,415,
%T A167178 2516,10017,2518,10019,120,10021,25022,100023,12524,825,25026,100027,
%U A167178 12528,100029,1030,100031,12532,100033,25034,4035,12536,100037,25038
%N A167178 a(n)^3 ends in n^3.
%C A167178 a(n) = least nontrivial k>n such that the decimal expansion of k^3 ends in n^3.
%e A167178 a(0)=10 because 10^3=1000 ends in 0^3=0
%e A167178 a(1)=11 because 11^3=1331 ends in 1^3=1
%e A167178 a(2)=12 because 12^3=1728 ends in 2^3=8
%e A167178 a(3)=103 because 103^3=1092727 ends in 3^3=27
%e A167178 a(4)=54 because 54^3=157464 ends in 4^3=64.
%Y A167178 Cf. A090292 Least nontrivial square whose decimal expansion ends in n^2,
%Y A167178 A090293 Least nontrivial k such that the decimal expansion of k^2 ends in n^2.
%K A167178 base,nonn,new
%O A167178 0,1
%A A167178 Zak Seidov (zakseidov(AT)yahoo.com), Oct 29 2009

%I A167177
%S A167177 1,2,2,5,5,7,13,2,29,19,47,68,43,151,31,246,237,267,611,34,
%T A167177 1078,707,1327,2149,701,4118,1760,5611,6904,4361,14463
%V A167177 1,-2,-2,5,5,-7,-13,2,29,19,-47,-68,43,151,31,-246,-237,267,611,-34,
%W A167177 -1078,-707,1327,2149,-701,-4118,-1760,5611,6904,-4361,-14463
%N A167177 Inverse toral expansion of:p(x)=(1+x+x^2)^2*(1+x+x^3)^3
%C A167177 The resoning in the Galois polynomial model:
%C A167177 1/alpha is about 137=Prime[33]
%C A167177 I realized that
%C A167177 33=2^5+2+1
%C A167177 was of the form
%C A167177 x^5+x+1
%C A167177 which is the Galois field polynomial for
%C A167177 GF[2^5] which has 32 elements.
%C A167177 Suppose that we take the standard model of physics
%C A167177 symmetry breaking as a GF[2^5] breaking;
%C A167177 GF[2^5]=>GF[2^2]^2*GF[2^3]^3
%C A167177 32->2*4+3*8
%C A167177 Since these are Abelian fields, this is really a different
%C A167177 way of looking at the standard model that is still 5d
%C A167177 and hyperbolic in time and space.
%C A167177 In polynomial terms that is one variable x0 going to five;
%C A167177 x0^5+x0+1-> {t^2+t+1,tau^2+tau+1,x^3+x+1,y^3+y+1,z^3+z+1}
%C A167177 I ,then, substitute back x for all the variables
%C A167177 and make a product polynomial.
%F A167177 1/(1 + 2 x + 6 x^2 + 11 x^3 + 19 x^4 + 27 x^5 + 34 x^6 + 38 x^7 + 36 x^8 + 30 x^9 + 21 x^10 + 12 x^11 + 5 x^12 + x^13)
%t A167177 a = {t^2 + t + 1, tau^2 + tau + 1, x^3 + x + 1, y^3 + y + 1, z^3 + z + 1} /. y -> x /. z -> x /. t -> x /. tau -> x
%t A167177 p[x_] = Product[a[[n]], {n, 1, 5}]
%t A167177 q[x_] = Expand[x^13*p[1/x]]
%t A167177 Table[ SeriesCoefficient[ Series[1/q[x], {x, 0, 30}], n], {n, 0, 30}]
%K A167177 sign,uned,new
%O A167177 0,2
%A A167177 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Oct 29 2009

%I A167176
%S A167176 0,1,8,0,1,8,0,1,8,0,1,8,0,1,8,0,1,8,0,1,8,0,1,8,0,1,8,0,1,8,0,1,8,0,1,
%T A167176 8,0,1,8,0,1,8,0,1,8,0,1,8,0,1,8,0,1,8,0,1,8,0,1,8,0,1,8,0,1,8,0,1,8,0,
%U A167176 1,8,0,1,8,0,1,8,0,1,8,0,1,8,0,1,8,0,1,8,0,1,8,0,1,8,0,1,8,0,1,8,0,1,8
%N A167176 n^3 mod 9
%C A167176 Essentially a duplicate of A021559. - njas, Oct 30 2009
%o A167176 (Other) sage: [power_mod(n,3,9 )for n in xrange(0, 105)] #
%K A167176 nonn,new
%O A167176 0,3
%A A167176 Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 29 2009

%I A167175
%S A167175 1,2,3,5,7,11,13,16,17,19,23,24,29,31,36,37,40,41,43,47,53,54,56,59,60,
%T A167175 61,64,67,71,73,79,81,83,84,88,89,90,86,97,100,101,103,104,107,109,112,
%U A167175 113,124,126,127,131,132,135,136,137,139,140,147,149,150,151,152,153
%N A167175 Numbers with a nonprime number of prime divisors (counted with multiplicity).
%Y A167175 Cf. A001222, A063989, A141468.
%K A167175 nonn,new
%O A167175 1,2
%A A167175 Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Oct 29 2009

%I A167172
%S A167172 1,1,1,1,2,1,1,3,3,1,1,4,7,4,1,1,5,11,11,5,1,1,6,16,25,16,6,1,1,7,22,40,
%T A167172 40,22,7,1,1,8,29,61,93,61,29,8,1,1,9,37,89,149,149,89,37,9,1,1,10,46,
%U A167172 125,233,371,233,125,46,10,1
%N A167172 A symmetrical triangular sequence:t[n,k]=Binomial[n, k] + A140356[n, k] - 1
%C A167172 Row sums are:
%C A167172 {1, 2, 4, 8, 17, 34, 71, 140, 291, 570, 1201,...}
%F A167172 t[n,k]=Binomial[n, k] + A140356[n, k] - 1
%F A167172 =Binomial[n, k] + If[k less than equal Floor[n/2], Gamma[k + 1], Gamma[n - k + 1]] - 1
%e A167172 {1},
%e A167172 {1, 1},
%e A167172 {1, 2, 1},
%e A167172 {1, 3, 3, 1},
%e A167172 {1, 4, 7, 4, 1},
%e A167172 {1, 5, 11, 11, 5, 1},
%e A167172 {1, 6, 16, 25, 16, 6, 1},
%e A167172 {1, 7, 22, 40, 40, 22, 7, 1},
%e A167172 {1, 8, 29, 61, 93, 61, 29, 8, 1},
%e A167172 {1, 9, 37, 89, 149, 149, 89, 37, 9, 1},
%e A167172 {1, 10, 46, 125, 233, 371, 233, 125, 46, 10, 1
%t A167172 t[n_, k_] = Binomial[n, k] + If[k <= Floor[n/2], Gamma[k + 1], Gamma[n - k + 1]] - 1
%t A167172 Flatten[Table[Table[t[n, k], {k, 0, n}], {n, 0, 10}]]
%Y A167172 A140356
%K A167172 nonn,uned,new
%O A167172 0,5
%A A167172 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Oct 29 2009

%I A167171
%S A167171 2,3,5,6,7,10,11,13,14,15,17,19,21,22,23,26,29,31,33,34,35,37,38,39,41,
%T A167171 43,46,47,51,53,55,57,58,59,61,62,65,67,69,71,73,74,77,79,82,83,85,86,
%U A167171 87,89,91,93,94,95,97,101,103,106,107,109,111,113,115,118,119,122,123
%N A167171 d(n)=2*omega(n).
%C A167171 Numbers n such that half of number of divisors of n is equal to number of distinct primes dividing n.
%e A167171 a(1)=2 (d(2)=2*omega(2)); a(2)=3 (d(3)=2*omega(3)).
%p A167171 omega := proc(n) if n = 1 then 0 ; else nops( numtheory[factorset](n)) ; end if; end proc: isA167171 := proc(n) numtheory[tau](n) = 2*omega(n) ; end proc: for n from 1 to 300 do if isA167171(n) then printf("%d,",n) ; end if ; end do: [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 31 2009]
%Y A167171 Cf. A000005, A000027, A001221.
%K A167171 nonn,new
%O A167171 1,1
%A A167171 Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Oct 29 2009
%E A167171 Corrected by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 31 2009

%I A167170
%S A167170 14,21,22,23,24,25,26,39,40,45,46,47,48,49,50,51,52,53,54,55,56,57,58,
%T A167170 87,90,91
%N A167170 a(6)=14, for n>=7, a(n)=a(n-1)+gcd(n, a(n-1))
%C A167170 For every n>=7, a(n)-a(n-1) is 1 or prime. This Roland-like "generator of primes" is different from A106108 (see comment to A167168)
%D A167170 E. S. Rowland, A natural prime-generating recurrence , Journal of Integer Sequences, Vol.11(2008), Article 08.2.8
%H A167170 V.Shevelev, <a href="http://arXiv.org/abs/math.0910.4676">A new generator of primes based on the Rowland idea</a>
%Y A167170 A167168 A106108 A132199 A167054 A167053 A166944 A166945 A163960 A163961 A163963 A084662 A084663 A134162 A135506 A135508 A118679 A120293
%K A167170 nonn,new
%O A167170 6,1
%A A167170 Vladimir Shevelev (shevelev(AT)bgu.ac.il), Oct 29 2009

%I A167169
%S A167169 1,3,7,36,1131
%N A167169 a(n) is the number of isomorphism classes of iterated quadratic extensions of the field of rationals of degree 2^i.
%e A167169 ex : a(1)=3 since Q[X]/(X^2-z) ramifies only at 2 iff z= -1, 2, -2 (up to squares).
%K A167169 nonn,new
%O A167169 0,2
%A A167169 G. Collinet (collinet.g(AT)gmail.com), Oct 29 2009

%I A167168
%S A167168 2,7,17,19,37,43,53
%N A167168 Primes p which produce the following different Rowland-like generators of primes: if N_p(p-1)=2p and, for n>=p, N_p(n)=N_p(n-1)+gcd(n, N_p(n-1)), then for every n>=p, N_p(n)-N_p(n-1) is 1 or prime
%C A167168 Put a(1)=2. Note that, for n>=3, N_2(n)=A106108(n). The least p>2 for which N_2(p-1) does not equal to 2p is 7, therefore a(2)=7. The least p>7, for which N_2(p-1) and N_7(p-1) are different from 2p, is 17, therefore a(3)=17, etc.
%D A167168 E. S. Rowland, A natural prime-generating recurrence , Journal of Integer Sequences, Vol.11(2008), Article 08.2.8
%H A167168 V.Shevelev, <a href="http://arXiv.org/abs/math.0910.4676">A new generator of primes based on the Rowland idea</a>
%Y A167168 A106108 A132199 A167054 A167053 A166944 A166945 A163960 A163961 A163963 A084662 A084663 A134162 A135506 A135508 A118679 A120293
%K A167168 nonn,uned,new
%O A167168 1,1
%A A167168 Vladimir Shevelev (shevelev(AT)bgu.ac.il), Oct 29 2009

%I A152616
%S A152616 30,40,54,350,380,414,500,532,544,558,608,620,644,666,726,740,1372,2002,
%T A152616 2190,2368,2370,2490,2624,2670,2910,3030,3090,3162,3210,3250,3270,3390,
%U A152616 3410,3430,3810,3880,3930,4040,4110,4120,4170,4280,4360,4470,4520,4530
%N A152616 Numbers n with property that exactly three subsets of proper divisors of n sum to n.
%C A152616 Or numbers n such that A065205(n)=3.
%e A152616 n=30: proper divisors of 30 = {1,2,3,5,6,10,15} and
%e A152616 30=5+10+15=2+3+10+15=1+3+5+6+15.
%Y A152616 Cf. A064771, A065205, A065235, A152615.
%K A152616 nonn,new
%O A152616 1,1
%A A152616 Zak Seidov (zakseidov(AT)yahoo.com), Oct 29 2009

%I A152615
%S A152615 12,18,42,56,66,100,176,196,208,348,372,444,460,492,516,550,564,580,636,
%T A152615 708,732,736,738,774,804,812,820,846,852,868,876,928,948,954,968,992,
%U A152615 996,1036,1062,1068,1098,1148,1164,1204,1206,1212,1236,1278,1284,1308
%N A152615 Numbers n with property that exactly two subsets of proper divisors of n sum to n.
%e A152615 n=12: proper divisors of 12 = {1,2,3,4,6} and 12=2+4+6=1+2+3+6.
%Y A152615 Cf. A064771, A065205, A065235.
%K A152615 nonn,new
%O A152615 1,1
%A A152615 Zak Seidov (zakseidov(AT)yahoo.com), Oct 29 2009

%I A167166
%S A167166 0,1,0,11,0,13,0,7,0,9,0,3,0,5,0,15,0,1,0,11,0,13,0,7,0,9,0,3,0,5,0,15,
%T A167166 0,1,0,11,0,13,0,7,0,9,0,3,0,5,0,15,0,1,0,11,0,13,0,7,0,9,0,3,0,5,0,15,
%U A167166 0,1,0,11,0,13,0,7,0,9,0,3,0,5,0,15,0,1,0,11,0,13,0,7,0,9,0,3,0
%N A167166 n^7 mod 16.
%o A167166 (Other) sage: [power_mod(n,7,16)for n in xrange(0, 93)] #
%K A167166 nonn,new
%O A167166 0,4
%A A167166 Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 29 2009

%I A167165
%S A167165 0,0,10,0,0,4,0,0,19,272,0,60,2,0,0,14,0,16,0,0,19,0,21,0,8,0,69,37,0,
%T A167165 302158,107,24,0,0,366,20,0,129,0,105,0,0,0,153,0,0,917,0,129,31,0,50,0,
%U A167165 52,27,0,55,77,0,0,59,0,61,0,0,64,0,0,0,743,0,0,71,0,73,0,0,76,26,0,0
%N A167165 Total distance which n is "catapulted" in the generation of the Catapult Sequence (A167161).
%C A167165 Whether or not this sequence is defined for all n depends on whether
%C A167165 or not A167161 is a true permutation of the non-negative integers
%C A167165 (see comments under A167161).
%H A167165 Andrew Weimholt, <a href="b167165.txt">Table of n, a(n) for n = 1..2000</a>
%e A167165 a(2) = 10, because 2 is catapulted by 1, 3, and 6 for a total
%e A167165 distance of 1+3+6 = 10
%Y A167165 Cf. A167161 The Catapult Sequence.
%Y A167165 Cf. A167162 The inverse permutation (conjectured) of A167161.
%Y A167165 Cf. A167163 number of times n is catapulted in generation of A167161.
%Y A167165 Cf. A167164 number catapulted by n in generation of A167161.
%K A167165 nonn,new
%O A167165 0,3
%A A167165 Andrew Weimholt (andrew(AT)weimholt.com), Oct 29 2009

%I A167164
%S A167164 1,2,12,2,5,9,2,8,24,210,11,57,8,9,15,27,17,30,11,20,35,22,27,9,31,26,
%T A167164 78,54,29,219348,37,49,11,34,303,29,37,130,39,117,9,30,43,153,26,46,719,
%U A167164 48,117,30,51,89,53,92,43,56,97,43,34,60,104,62,107,37,65,112,57,39
%N A167164 The number which is "catapulted" by n in the generation of the Catapult Sequence (A167161).
%C A167164 Whether or not this sequence is defined for all n depends on whether
%C A167164 or not A167161 is a true permutation of the non-negative integers
%C A167164 (see comments under A167161).
%H A167164 Andrew Weimholt, <a href="b167164.txt">Table of n, a(n) for n = 1..2000</a>
%e A167164 a(2) = 12, because in the generation of the A167161,
%e A167164 2 eventually catapults 12.
%Y A167164 Cf. A167161 The Catapult Sequence.
%Y A167164 Cf. A167162 The inverse permutation (conjectured) of A167161.
%Y A167164 Cf. A167163 number of times n is catapulted in generation of A167161.
%Y A167164 Cf. A167165 total distance which n is catapulted in generation of A167161.
%K A167164 nonn,new
%O A167164 0,2
%A A167164 Andrew Weimholt (andrew(AT)weimholt.com), Oct 29 2009

%I A167163
%S A167163 0,1,3,0,0,1,0,0,2,6,0,3,1,0,0,1,0,1,0,0,1,0,1,0,1,0,2,2,0,17,3,1,0,0,4,
%T A167163 1,0,3,0,2,0,0,0,3,0,0,5,0,2,1,0,1,0,1,1,0,1,2,0,0,1,0,1,0,0,1,0,0,0,4,
%U A167163 0,0,1,0,1,0,0,1,1,0,0,1,0,0,5,0,5,0,1,2,0,1,3,0,1,0,1,2,0,1
%N A167163 Number of times n is "catapulted" in generation of the Catapult Sequence (A167161).
%H A167163 Andrew Weimholt, <a href="b167163.txt">Table of n, a(n) for n = 1..2000</a>
%e A167163 a(2) = 3, because in generating A167161, the number 2 is catapulted
%e A167163 3 times (first by 1, then by 3, and finally by 6).
%Y A167163 Cf. A167161 The Catapult Sequence.
%Y A167163 Cf. A167162 The inverse permutation (conjectured) of A167161.
%Y A167163 Cf. A167164 number catapulted by n in generation of A167161.
%Y A167163 Cf. A167165 total distance which n is catapulted in generation of A167161.
%K A167163 nonn,new
%O A167163 0,3
%A A167163 Andrew Weimholt (andrew(AT)weimholt.com), Oct 29 2009

%I A167162
%S A167162 0,1,8,2,3,6,4,5,17,152,7,41,10,9,11,19,12,21,13,14,25,15,27,16,22,18,
%T A167162 57,39,20,159537,78,35,23,24,218,36,26,94,28,84,29,30,31,112,32,33,525,
%U A167162 34,104,52,37,64,38,66,54,40,69,82,42,43,74,44,76,45,46,80,47,48,49,443
%N A167162 Inverse Permutation (conjectured) of Catapult Sequence (A167161).
%C A167162 Whether or not this sequence is defined for all n depends on whether
%C A167162 or not A167161 is a true permutation of the non-negative integers
%C A167162 (see comments under A167161).
%H A167162 Andrew Weimholt, <a href="b167162.txt">Table of n, a(n) for n = 0..2000</a>
%e A167162 a(2) = 8 because A167161(8) = 2.
%Y A167162 Cf. A167161 The Catapult Sequence.
%Y A167162 Cf. A167163 number of times n is catapulted in generation of A167161.
%Y A167162 Cf. A167164 number catapulted by n in generation of A167161.
%Y A167162 Cf. A167165 total distance which n is catapulted in generation of A167161.
%K A167162 nonn,new
%O A167162 0,3
%A A167162 Andrew Weimholt (andrew(AT)weimholt.com), Oct 29 2009

%I A166570
%S A166570 2,7,9,11,12,16,17,22,23,24,26,27,30,32,33,37,42,43,44,45,47,50,51,52,
%T A166570 55,57,58,60,62,63,64,65,66,67,70,72,74,76,77,79,82,83,86,87,88,89,92,
%U A166570 93,94,97,99,100,102,103,105,107,110,111,112,114,115,116,117,121,122
%N A166570 Numbers n such that 12*n+11 is not prime
%C A166570 n=(p^2+2*p-11)/12 mod.(p); or n=(p^2+10*p-11)/12 mod.(p);
%e A166570 for p=5, n((5^2+2*5-11)/12=2 (7,12,17,22,27,32,37 and so on); for p=7, n=(7^2+10*7-11)/12=9 (16,23,30,37,44,51,58 and so on)
%Y A166570 Cf. A167057
%K A166570 nonn,new
%O A166570 1,1
%A A166570 Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Oct 29 2009

%I A167161
%S A167161 0,1,3,4,6,7,5,10,2,13,12,14,16,18,19,21,23,8,25,15,28,17,24,32,33,20,
%T A167161 36,22,38,40,41,42,44,45,47,31,35,50,52,27,55,11,58,59,61,63,64,66,67,
%U A167161 68,70,71,49,73,54,75,76,26,79,80,82,83,85,87,51,90,53,93,95,56,98,78
%N A167161 The Catapult Sequence
%C A167161 This sequence is conjectured to be a permutation of the non-negative
%C A167161 integers, generated by the following process:
%C A167161 Begin with the non-negative integers in their normal positions.
%C A167161 Starting with n=0, the number in position n, which will be our a(n),
%C A167161 "catapults" the neighbor to its right a(n) spaces further to the
%C A167161 right. Increment n and repeat.
%C A167161 Whether or not this is actually a permutation of the non-negative
%C A167161 integers depends on whether or not there exists a number that is
%C A167161 catapulted an infinite number of times. If such a number (say X)
%C A167161 exists, the inverse "permutation" will be undefined at the Xth term.
%H A167161 Andrew Weimholt, <a href="b167161.txt">Table of n, a(n) for n = 0..2000</a>
%e A167161 step 0: a(0)=0 catapults 1 a distance of 0 -> 0,1,2,3,4,5,6,7,8
%e A167161 step 1: a(1)=1 catapults 2 a distance of 1 -> 0,1,3,2,4,5,6,7,8
%e A167161 step 2: a(2)=3 catapults 2 a distance of 3 -> 0,1,3,4,5,6,2,7,8
%e A167161 step 3: a(3)=4 catapults 5 a distance of 4 -> 0,1,3,4,6,2,7,8,5
%Y A167161 Cf. A167162 the inverse permutation (conjectured).
%Y A167161 Cf. A167163 number of times n is catapulted.
%Y A167161 Cf. A167164 number which is catapulted by n.
%Y A167161 Cf. A167165 total distance which n is catapulted.
%K A167161 nonn,new
%O A167161 0,3
%A A167161 Andrew Weimholt (andrew(AT)weimholt.com), Oct 29 2009

%I A166569
%S A166569 4,7,9,14,15,19,20,21,24,26,28,29,32,33,34,35,37,39,42,44,46,48,49,54,
%T A166569 55,56,58,59,63,64,66,69,70,72,74,77,78,79,81,83,84,85,89,91,92,94,95,
%U A166569 96,98,99,100,101,103,104,105,109,111,112,113,114,115,117,119,124,125
%N A166569 Numbers n such that 12*n+7 is not prime.
%C A166569 n=(p^2+6*p-7)/12 mod.(p)
%e A166569 For p=5, n=(5^2+6*5-7)/12=4 (9,14,19,24,29,34,39 and so on) for p=7, n=(7^2+6*7-7)/12=7 (14,21,28,35,42,49,56 and so on) for p=11, n=(11^2+6*11-7)/12=15 (26,37,48,59,70,81,92 an so on)
%Y A166569 Cf. A167056
%K A166569 nonn,new
%O A166569 1,1
%A A166569 Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Oct 29 2009

%I A166507
%S A166507 0,10,1023,2676,16867,111688
%N A166507 Least n-comma number: smallest nonnegative integer that occurs in the sequence S[k+1]=S[k]+10*last_digit(S[k-1])+first_digit(S[k]) for at least n different splittings a(n)=concat(S[0],S[1]).
%C A166507 This subsequence of A166508 and of A166511 consists in the least numbers (= nonnegative integers) a(n) which occur as term in the sequence S(a,b), defined by S[0]=a, S[1]=b, S[k+1]=S[k]+10*last_digit(S[k-1])+first_digit(S[k]), for at least n legal splittings a(n)=concat(a,b).
%C A166507 "Legal" means that a and b have at least one digit each, and b has no leading zero(s) (unless b=0). Therefore a(n) must have at least n nonzero digits preceding the last digit (cf. formula). See A166511 and A166512 for more information.
%H A166507 E. Angelini, <a href="http://www.cetteadressecomportecinquantesignes.com/Commatile.htm">k-comma numbers</a>, Oct. 2009.
%F A166507 a(k) >= [10^k/9]*10 = (10^(k+1)-1)/9-1
%e A166507 There are 0 ways to split a(0)=0 in two substrings, so this is the smallest 0-comma number.
%e A166507 The number a(1)=10 is the smallest (1-)comma number, cf. A166511.
%e A166507 The number a(2)=1023 is the smallest 2-comma number: it occurs in S(10,23) and in S(102,3), cf. A166512.
%o A166507 (PARI) A166507(k) = { my(a,b,c); for( n=10^k\9*10,1e9, c=k; n%100 | next; for(d=1,#Str(n)-1, d+c>#Str(n) & break /* not possible: next n */; a=n\10^d, b=n%10^d; b<10^(d-1) & d>1 & next /* not legal: next d */; while(n > b=10*(a%10)+b\10^(#Str(b)-1)+a=b,); b>n & next; c-- | return(n)))}
%Y A166507 Cf. A166508, A166511, A166512, A166513.
%K A166507 base,hard,more,nonn,new
%O A166507 0,2
%A A166507 E. Angelini (Eric.Angelini(AT)kntv.be) and M. F. Hasler (MHasler(AT)univ-ag.fr), Oct 29 2009

%I A166563
%S A166563 5,6,10,13,15,17,18,20,25,27,28,30,31,34,35,36,39,40,41,44,45,48,50,52,
%T A166563 55,57,59,60,61,62,65,69,70,72,74,75,76,80,82,83,85,86,89,90,93,94,95,
%U A166563 96,97,100,103,104,105,109,110,111,112,115,116,118,120,121,122,125,126
%N A166563 Numbers n such that 12*n+5 is not prime
%C A166563 n=(p^2+4p-5)/12 mod.(p), or n=(p^2+8p-5)/12 mod.(p)
%e A166563 For p=5, n=(5^2+8*5-5)/12=5 (10,15,20,25,30,35 and so on); for p=7, n=(7^2+4*7-5)/12=6 (13,20,27,34,41,48 and so on): for p=11, n=(11^2+8*11-5)/12=17 (28,39,50,61,72,83,94 and so on)
%Y A166563 Cf. A167055
%K A166563 nonn,new
%O A166563 1,1
%A A166563 Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Oct 29 2009

%I A166508
%S A166508 1,2,3,4,5,6,7,8,9,10,20,30,40,50,60,70,80,90,109,806,1023,1044,2005,
%T A166508 2676,3066,3602,4051,6053,6246,8011,8349,9427,10022,10074,10587,13090,
%U A166508 15031,16867,20088,20699,21698,23108,29986,30091,30306,32226,40022
%N A166508 Hypercomma numbers: n occurs in the sequence S[k+1]=S[k]+10*last_digit(S[k-1])+first_digit(S[k]) for each "legal" splitting n=concat(S[0],S[1]).
%C A166508 This subsequence of A166511 consists in the numbers which occur as term in the sequence S(a,b), defined by S[0]=a, S[1]=b, S[k+1]=S[k]+10*last_digit(S[k-1])+first_digit(S[k]), for any legal splitting n=concat(a,b).
%C A166508 "Legal" means that a and b have at least one digit each, and b has no leading zero(s) (unless b=0). See A166511 and A166512 for more information.
%C A166508 They are called hypercomma numbers because they are k-comma numbers (cf. A166507) with k as large as possible for the given number of (zero and nonzero) digits, or "phenix" numbers because they can be cut into (two) pieces is any (legal) way and will be "reborn" as a whole out of the "pieces".
%H A166508 E. Angelini, <a href="http://www.cetteadressecomportecinquantesignes.com/Commatile.htm">k-comma numbers</a>, Oct. 2009.
%e A166508 There is no legal way to split the single digit numbers 1...9, therefore they are included.
%e A166508 More generally, a k-comma number which has exactly k nonzero digits when the last digit is ignored, will be in this sequence: e.g. 2005 can only be cut as (200,5); 10022 can only be cut as (1002,2) and (100,22), and it is a 2-comma number (A166512).
%o A166508 (PARI) {for(n=1,1e5,/*is_A166508(n)=*/ n%100 & for(d=1,#Str(n)-1, my( a=n\10^d, b=n%10^d ); b<10^(d-1) & d>1 & next /* not legal */; while(n > b=10*(a%10)+b\10^(#Str(b)-1)+a=b,); b>n & next(2) /* bad */); print1(n", "))}
%Y A166508 Cf. A166507, A166511, A166512, A166513.
%K A166508 base,nonn,new
%O A166508 1,2
%A A166508 E. Angelini (Eric.Angelini(AT)kntv.be) and M. F. Hasler (MHasler(AT)univ-ag.fr), Oct 29 2009

%I A167160
%S A167160 0,0,0,0,1,0,1,1,2,1,5,2,8,5,12,8,25,13,30,23,51,33,76,51,109,78,144,
%T A167160 106,218,150,274,212,382,279,499,366,650,493,815,623,1083,800,1305,1020,
%U A167160 1653,1261,2045,1554,2505,1946,3008,2322,3713,2829,4354,3418,5233,4063
%N A167160 Number of 8-hedrites with 2 <= n <= 70.
%C A167160 From table 1 on p.5 of Sikiric, who abstracts: an i-hedrite is a 4-regular plane graph with faces of size 2, 3 and 4. We do a short survey of their known properties and explain some new algorithms that allow their efficient enumeration. Using this we give the symmetry groups of all i-hedrites and the minimal representative for each. We also review the link of 4-hedrites with knot theory and the classification of 4-hedrites with simple central circuits. An i-self-hedrite is a self-dual plane graph with faces and vertices of size/degree 2, 3 and 4. We give a new efficient algorithm for enumerating them based on i-hedrites. We give a classification of their possible symmetry groups and a classification of 4-self-hedrites of symmetry T, Td in terms of the Goldberg-Coxeter construction. Then we give a method for enumerating 4-self-hedrites with simple zigzags.
%H A167160 Mathieu Dutour Sikiric, Michel Deza, <a href="http://arxiv.org/abs/0910.5323">4-regular and self-dual analogs of fullerenes</a>, Oct 28, 2009.
%Y A167160 Cf. A167156-A167160
%K A167160 nonn,new
%O A167160 2,9
%A A167160 Jonathan Vos Post (jvospost3(AT)gmail.com), Oct 29 2009

%I A167149
%S A167149 1,10000,29997,59992,99985,149976,209965,279952,359937,449920,549901,
%T A167149 659880,779857,909832,1049805,1199776,1359745,1529712,1709677,1899640,
%U A167149 2099601,2309560,2529517,2759472,2999425,3249376,3509325,3779272
%N A167149 These numbers are 10000-gonal numbers. The formula for 10000-gonal numbers is a(n) = n + 4999 * n * (n-1).
%F A167149 a(n)=3*a(n-1)-3*a(n-2)+a(n-3). G.f.: x*(1+9997*x)/(1-x)^3. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 02 2009]
%e A167149 Example: For n=13 , a(n)=779857
%p A167149 P := proc(n,k) n*((k-2)*n-k+4)/2 ; end: A167149 := proc(n) P(n,10000) ; end: seq(A167149(n),n=1..50) ; [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 02 2009]
%Y A167149 Cf. A057145. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 02 2009]
%K A167149 nonn,new
%O A167149 1,2
%A A167149 Michael G. Fenner (sidk.20c(AT)gmail.com), Oct 28 2009
%E A167149 Edited (but not checked) by njas, Nov 01 2009
%E A167149 Sequence extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 02 2009

%I A166513
%S A166513 2676,6246,8349,9427,10587,11558,11756,11811,12427,12788,13090,13110,
%T A166513 14328,15031,15187,15493,15637,16867,18322,18768,19918,20699,21138,
%U A166513 21422,21698,22824,23108,23242,23868,24456,24854,25342,25478,26583
%N A166513 3-comma numbers: n occurs in the sequence S[k+1]=S[k]+10*last_digit(S[k-1])+first_digit(S[k]) for three different splittings n=concat(S[0],S[1]).
%C A166513 This subsequence of A166512 consists in the numbers that can be split up in (at le