Search: id:A001477
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%I A001477
%S A001477 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,
%T A001477 26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,
               49,
%U A001477 50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,
               73,74,75,76,77
%N A001477 The nonnegative integers.
%C A001477 For nonnegative n, partial sums of A057427 = Sign(n). - Jeremy Gardiner 
               (jeremy.gardiner(AT)btinternet.com), Sep 08 2002
%C A001477 Contribution from Eric Desbiaux (moongerms(AT)wanadoo.fr), Oct 28 2008: 
               (Start)
%C A001477 (APSO) Alternating partial sums of
%C A001477 (a-b+c-d+e-f+g...)=(a+b+c+d+e+f+g...)-2*(b+d+f...)
%C A001477 it appears that APSO A001477 =
%C A001477 A001057 = A000217 - 2*(A008794)
%C A001477 (End)
%C A001477 A001477 = A000040 U A141468. [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), 
               Jul 28 2009]
%C A001477 Or, zero together with natural numbers A000027; also A001477 = A002808 
               U A158611. [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Sep 
               27 2009]
%C A001477 Also, n minus smallest divisor of n; or A001477 = A005097 U A047845. 
               [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Oct 09 2009]
%C A001477 Largest number<nth natural number. A001477 = A167706 U A167707. [From 
               Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Nov 10 2009]
%C A001477 Contribution from Eric Desbiaux (moongerms(AT)wanadoo.fr), Nov 15 2009: 
               (Start)
%C A001477 It appears that, with the Bachet-Bezout theorem, A001477 = (2*A080425) 
               + (3*A008611)
%C A001477 and A000040 = (2*(3-A039701)) + (3*A157733) = 6 - 2*A039701 + 3*A157733,
%C A001477 implicating the Fundamental Theorem of Arithmetic.
%C A001477 (End)
%D A001477 Paul Barry, A Catalan Transform and Related Transformations on Integer 
               Sequences, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.5.
%H A001477 N. J. A. Sloane, <a href="b001477.txt">Table of n, a(n) for n = 0..500000</
               a>
%H A001477 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas 
               for Some Functions on Finite Sets</a>
%H A001477 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%H A001477 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               NaturalNumber.html">Natural Number</a>
%H A001477 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               NonnegativeInteger.html">Nonnegative Integer</a>
%H A001477 Robert G. Wilson v, <a href="a001477.txt">American English names for 
               the numbers from 0 to 100999 without spaces or hyphens</a>.
%H A001477 <a href="Sindx_Cor.html#core">Index entries for "core" sequences</a>
%H A001477 <a href="Sindx_Per.html#IntegerPermutation">Index entries for sequences 
               that are permutations of the natural numbers</a>
%H A001477 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%F A001477 a(n)=n; a(0) = 0, a(n) = a(n-1)+1; G.f.: x/(1-x)^2.
%F A001477 Multiplicative with a(p^e) = p^e. - David W. Wilson (davidwwilson(AT)comcast.net), 
               Aug 01, 2001.
%F A001477 When seen as array: T(k, n) = n + (k+n)*(k+n+1)/2. Main diagonal is 2n(n+1) 
               (A046092), antidiagonal sums are n(n+1)(n+2)/2 (A027480). - Ralf 
               Stephan, Oct 17 2004
%F A001477 Dirichlet generating function: zeta(s-1). - Franklin T. Adams-Watters, 
               Sep 11 2005.
%F A001477 E.g.f. x*e^x. - Franklin T. Adams-Watters, Sep 11 2005.
%F A001477 a(0)=0, a(1)=1, a(n)=2a(n-1)-a(n-2). - Jaume Oliver i Lafont (joliverlafont(AT)gmail.com), 
               May 07 2008
%F A001477 a(n)=n-1 for n>0. [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), 
               Sep 27 2009]
%F A001477 a(n)=A000027(n)-A000012(n). [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), 
               Oct 09 2009]
%p A001477 [ seq(n,n=0..100) ];
%t A001477 Table[n, {n, 0, 100}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), 
               Apr 08 2006
%o A001477 (MAGMA) [ n : n in [0..100]];
%o A001477 (Other) sage: [log(e^n)for n in xrange(0,78)]# [From Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Jun 03 2009]
%o A001477 (PARI) A001477(n)=n /* first term is a(0) */
%Y A001477 Cf. A000027.
%Y A001477 Sequence in context: A119972 A131738 A000027 this_sequence A087156 A033619 
               A130734
%Y A001477 Adjacent sequences: A001474 A001475 A001476 this_sequence A001478 A001479 
               A001480
%K A001477 core,nonn,easy,mult,tabl,new
%O A001477 0,3
%A A001477 N. J. A. Sloane (njas(AT)research.att.com).
%E A001477 Duplicate formula removed by Michael Porter (michael_b_porter(AT)yahoo.com), 
               Nov 02 2009

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