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A175865 Numbers k with property that 2^(k-1) == 1 (mod k) and 2^((3*k-1)/2) - 2^((k-1)/2) + 1 == 0 (mod k). 6
3, 5, 11, 13, 19, 29, 37, 43, 53, 59, 61, 67, 83, 101, 107, 109, 131, 139, 149, 157, 163, 173, 179, 181, 197, 211, 227, 229, 251, 269, 277, 283, 293, 307, 317, 331, 347, 349, 373, 379, 389, 397, 419, 421, 443, 461, 467, 491, 499, 509, 523, 541, 547, 557, 563 (list; graph; refs; listen; history; text; internal format)
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

Cf. A001262, A001567, A003629.

Sequence in context: A059646 A319041 A003629 * A001122 A152871 A329760

Adjacent sequences:  A175862 A175863 A175864 * A175866 A175867 A175868

KEYWORD

nonn

AUTHOR

Alzhekeyev Ascar M, Sep 30 2010

EXTENSIONS

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

STATUS

approved

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Last modified March 8 01:41 EST 2021. Contains 341934 sequences. (Running on oeis4.)