1,2

These are also the numbers that cannot be written as i*j + i + j (i,j >= 1) - Rainer Rosenthal (r.rosenthal(AT)web.de), Jun 24 2001; Henry Bottomley, Jul 06 2002

The values of k for which sum((-1)^j*binomial(k, j)*binomial(k-1-j, n-j)/(j+1), j=0..n) produces an integer for all n such that n < k. Setting k=10 yields [0, 1, 4, 11, 19, 23, 19, 11, 4, 1, 0] for n = [ -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9], so 10 is in the sequence. Setting k=3 yields [0, 1, .5, .5] for n = [ -1, 0, 1, 2], so 3 is not in the sequence. - Dug Eichelberger (dug(AT)mit.edu), May 14 2001

n such that x^n + x^(n-1) + x^(n-2) + ... + x + 1 is irreducible. - Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 22 2002.

Records for Euler totient function phi.

Using Wilson's theorem, also n such that (n+1) divides (n!+1) - Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 20 2002

n such that phi(n^2)==phi(n^2+n) - Jon Perry (perry(AT)globalnet.co.uk), Feb 19 2004

No palindromic prime can have an even number of digits except 11; this holds in any number base a(n), n>1. - Lekraj Beedassy (blekraj(AT)yahoo.com), Mar 07 2005

Numbers having only the trivial perfect partition consisting of a(n) 1's. - Lekraj Beedassy (blekraj(AT)yahoo.com), Jul 23 2006

Numbers n such that the sequence {binomial coefficient C(k,n), k >= n } contains exactly one prime. - Artur Jasinski (grafix(AT)csl.pl), Dec 02 2007

Record values of A143201: a(n)=A143201(A001747(n+1)) for n>1. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 12 2008]

Contribution from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 10 2009: (Start)

The first N terms can be generated by the following sieving process:

start with {1, 2, 3, 4, ..., N-1, N};

for i:=1 until SQRT(N) do

(if (i is not striked out) then

(for j:=2*i+1 step i+1 until N do

(strike j from the list)));

remaining numbers = {a(n): a(n)<=N}. (End)

a(n) = partial sums of A075526(n-1) = Sum_(1...n) A075526(n-1) = Sum_(1...n) [A008578(n+1) - A008578(n)] = Sum_(1...n) [A158611(n+1) - A158611(n)] for n >= 1. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Aug 04 2009]

Or, largest divisor of nth prime minus smallest divisor of nth prime. [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Sep 07 2009].

Also, phi(prime(n)); nth prime minus number of perfect partitions of nth prime. [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Oct 10 2009]

A006093 U A072668 = A000027. [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Oct 22 2009]

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Archimedeans Problems Drive, Eureka, 40 (1979), 28.

Problem E 3065, American Mathematical Monthly, 1984, p. 649.

Problem E 3065, American Mathematical Monthly, No. 4, 1987, pp. 378.

M. Gardner, The Colossal Book of Mathematics, pp. 31 W.W.Norton & Co. NY 2001.

M. Gardner, Mathematical Circus, pp. 251-2, Alfred A.Knopf NY 1979.

T. D. Noe, Table of n, a(n) for n=1..10000

Index entries for sequences generated by sieves [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 10 2009]

a(n)=A000040(n)-A000012(n). {From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Sep 07 2009].

a(n)=A000010(A000040(n))=A000040(n)-A002033(n). [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Oct 10 2009]

Table[Prime[n]-1, {n, 1, 30}] - Vladimir Orlovsky, Apr 27 2008

a(n) = K(n, 1) and A034693(K(n, 1)) = 1 for all n. The subscript n refers to this sequence and K(n, 1) is the index in A034693 - Labos E.

Cf. A000040, A034693, A034694. Different from A075728.

Complement of A072668 (composite numbers minus 1), A072670(a(n))=0.

Essentially the same as A039915.

Cf. A084920, A006093, A050997, A008864, A060800, A131991, A131992, A131993.

Cf. A000010, A000012, A002033. [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Oct 10 2009]

Sequence in context: A128984 A075728 A146886 this_sequence A127965 A117891 A072752

Adjacent sequences: A006090 A006091 A006092 this_sequence A006094 A006095 A006096

nonn,easy,nice

N. J. A. Sloane (njas(AT)research.att.com).