A308079 - OEIS

%I #21 Mar 31 2024 02:08:31

%S 10974881,193949641,717653129,8762386393,19683169273,24802217129,

%T 78618861353,121271968201,146050578391,169905267617,188684740591,

%U 232153956569,290762221753,306091598201,336675266287,394233108121,592050558553

%N Pseudoprimes to base 3 that divide a Mersenne number.

%C Members of A005935 that divide a member of A001348.

%C 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.

%C The known entries are proper divisors of a Mersenne number. It is not known if the Mersenne number itself can belong to this sequence.

%H Amiram Eldar, <a href="/A308079/b308079.txt">Table of n, a(n) for n = 1..202</a> (terms below 10^15)

%H Mersenne Forum, <a href="https://www.mersenneforum.org/showthread.php?p=516206#post516206">Composite PRP (discussion thread)</a>.

%e 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).

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

%Y Intersection of A005935 and A122094.

%Y Subsequence of A052155.

%Y Cf. A001348, A002326.

%K nonn

%O 1,1

%A _Jeppe Stig Nielsen_, May 11 2019