A308079 Pseudoprimes to base 3 that divide a Mersenne number.

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

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((k-1)/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.

Links

Amiram Eldar, Table of n, a(n) for n = 1..202 (terms below 10^15)

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)^(n-1)==1&&!ispseudoprime(n)&&ispseudoprime(znorder(Mod(2, n)))&&print1(n, ", "))

Crossrefs

Intersection of A005935 and A122094.

Subsequence of A052155.

Cf. A001348, A002326.

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