A079324 k such that 2kp+1 is the first factor of a nonprime Mersenne number M(p) = 2^p - 1.

1, 1, 4, 3, 163, 5, 25, 60, 1525, 1445580, 1609, 3, 17, 1, 59, 36793758459, 12379533, 3421967, 15, 1, 116905896337578232, 20236572837, 290792847537859675, 60, 2713800, 461, 7033, 2112, 1, 120, 1, 35807, 19, 413328944, 36, 41

Offset

1,3

Comments

a(188) = 216 = k = (f-1)/2p for p=1231, f=531793. Although Mersenne numbers with p = 1213, 1217, 1229, 1231 are not fully factored, we know their smallest factors. One factor is known for p=1237 but it is not certain that it is the smallest. - Gord Palameta, Sep 26 2018

Links

Gord Palameta, Table of n, a(n) for n = 1..188

Example

2^11 - 1 = 23*89, 23 = 2*1*11 + 1, therefore a(1) = 1.

Prog

(PARI) forprime (n=3, 101, v=2^n-1; if (!isprime(v), print1((factor(v)[, 1][1]-1)\(2*n)", ")))

Crossrefs

Cf. A054723.

Sequence in context: A351792 A362674 A325871 * A002298 A195565 A368301

Adjacent sequences: A079321 A079322 A079323 * A079325 A079326 A079327

Keyword

nonn

Author

Jon Perry, Feb 12 2003

Extensions

More terms from Michel Marcus, Mar 17 2014

Status

approved