

A175865


Numbers k with property that 2^(k1) == 1 (mod k) and 2^((3*k1)/2)  2^((k1)/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
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OFFSET

1,1


COMMENTS

All composites in this sequence are 2pseudoprimes, 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^(31)1 = 3 is divisible by 3, and 2^((3*31)/2)  2^((31)/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



