

A308079


Pseudoprimes to base 3 that divide a Mersenne number.


0



10974881, 193949641, 717653129, 8762386393, 19683169273, 24802217129, 78618861353, 121271968201, 146050578391, 169905267617, 188684740591, 232153956569, 290762221753, 306091598201, 336675266287, 394233108121, 592050558553
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OFFSET

1,1


COMMENTS

Members of A005935 that divide a member of A001348.
Odd members k of A005935 such that the multiplicative order of 2 modulo k is a prime. Odd members k of A005935 such that A002326((k1)/2) is prime.
The known entries are proper divisors of a Mersenne number. It is not known if the Mersenne number itself can belong to this sequence.
Subsequence of A052155.


LINKS

Table of n, a(n) for n=1..17.
Mersenne Forum, Composite PRP (discussion thread).


EXAMPLE

10974881 is in the sequence because it divides 2^239  1 (and 239 is prime), it is not a prime, but 3^10974880 === 1 (mod 10974881).


PROG

(PARI) forstep(n=3, +oo, 2, Mod(3, n)^(n1)==1&&!ispseudoprime(n)&&ispseudoprime(znorder(Mod(2, n)))&&print1(n, ", "))


CROSSREFS

Cf. A005935, A001348, A002326, A122094, A052155.
Sequence in context: A202470 A224639 A298704 * A114680 A329224 A274834
Adjacent sequences: A308076 A308077 A308078 * A308080 A308081 A308082


KEYWORD

nonn


AUTHOR

Jeppe Stig Nielsen, May 11 2019


STATUS

approved



