A057178 Numbers k such that (12^k + 1)/13 is a prime.

5, 11, 109, 193, 1483, 11353, 21419, 21911, 24071, 106859, 139739, 495953

Offset: 1

Author

N. J. A. Sloane, Sep 15 2000

Keywords

• nonn

Comments

(12^1483 + 1)/13, a 1600-digit number, has now been certified prime with Primo. - Rick L. Shepherd, May 01 2002

Links

• Paul Bourdelais, A Generalized Repunit Conjecture
• J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
• H. Dubner and T. Granlund, Primes of the Form (b^n+1)/(b+1), J. Integer Sequences, 3 (2000), #P00.2.7.
• H. Lifchitz, Mersenne and Fermat primes field
• Eric Weisstein's World of Mathematics, Repunit

Crossrefs

Different from A056265.

Programs

Mathematica

lst={};Do[p=(12^n+1)/13;If[PrimeQ[p], AppendTo[lst, n]], {n, 7!}];lst (* Vladimir Joseph Stephan Orlovsky, Sep 29 2008 *)

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 05 2008

a(10) corresponds to a probable prime, discovered by Paul Bourdelais, Feb 08 2010

a(11) corresponds to a probable prime, discovered by Paul Bourdelais, Sep 21 2011

a(12) corresponds to a probable prime, discovered by Paul Bourdelais, Nov 13 2018