A219341 Least prime k such that k*2^n + 1 divides 2^k - 1, or 0 if no such prime exists.

2, 3, 0, 11, 397, 839, 1459, 2081, 7297, 53849, 3499, 70589, 792277, 20399, 11173873, 929057, 232591, 6782759, 5834299, 26812151, 40269673, 88529891, 368454343, 616767917, 1167319801, 709939943, 38151887029, 38617336361, 23280518791, 168046587719, 882701485339

Offset: 0

Author

Arkadiusz Wesolowski, Nov 18 2012

Keywords

• nonn

Comments

If a(n) > 0, then a(n)*2^n + 1 is in A122094.

Links

• G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 232591
• Eric Weisstein's World of Mathematics, Mersenne Number

Crossrefs

Cf. A001348, A002144.

Programs

Mathematica

lst = {}; Do[k = 2; If[n == 2, AppendTo[lst, 0], While[True, If[PrimeQ[k], f = k*2^n + 1; If[PrimeQ[f] && PowerMod[2, k, f] == 1, AppendTo[lst, k]; Break[]]]; k++]], {n, 0, 13}]; lst

Extensions

a(26)-a(30) from Jason Yuen, May 24 2024