OFFSET

1,1

COMMENTS

All composites in this sequence are 2-pseudoprimes, see A001567.

The subsequence of composites begins: 3277, 29341, 49141, 80581, 88357, 104653, 196093, 314821, 458989, 476971, 489997, ..., . - Robert G. Wilson v, Oct 02 2010

The sequence includes all the primes of A003629. - Alzhekeyev Ascar M, Mar 09 2011

If we consider the composites in this sequence which are in the modulo classes == 3 (mod 8) or == 5 (mod 8), they are moreover strong pseudoprimes to base 2 (see A001262). - Alzhekeyev Ascar M, Mar 09 2011

Are there any composites in this sequence which are *not* in the two modulo classes == {3,5} (mod 8)? - R. J. Mathar, Mar 29 2011

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

EXAMPLE

3 is a term since 2^(3-1)-1 = 3 is divisible by 3, and 2^((3*3-1)/2) - 2^((3-1)/2) + 1 = 15 is divisible by 3.

MATHEMATICA

fQ[n_] := PowerMod[2, n - 1, n] == 1 && Mod[ PowerMod[2, (3 n - 1)/2, n] - PowerMod[2, (n - 1)/2, n], n] == n - 1; Select[ Range@ 570, fQ] (* Robert G. Wilson v, Oct 02 2010 *)

CROSSREFS

KEYWORD

nonn

AUTHOR

Alzhekeyev Ascar M, Sep 30 2010

EXTENSIONS

More terms from Robert G. Wilson v, Oct 02 2010

STATUS

approved