A052155 -id:A052155 - cp's OEIS frontend

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

Jeppe Stig Nielsen, May 11 2019

nonn

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.

			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).

Amiram Eldar, Table of n, a(n) for n = 1..202 (terms below 10^15)
Mersenne Forum, Composite PRP (discussion thread).

Intersection of A005935 and A122094.
Subsequence of A052155.
Cf. A001348, A002326.

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

cp's OEIS Frontend

A308079 Pseudoprimes to base 3 that divide a Mersenne number.

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