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]

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

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.

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

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

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

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).