A004064 Numbers k such that (12^k - 1)/11 is prime. (Formerly M0744)

2, 3, 5, 19, 97, 109, 317, 353, 701, 9739, 14951, 37573, 46889, 769543

Offset

1,1

Comments

Also, numbers k such that 12^k-1 is a semiprime. - Sean A. Irvine, Oct 16 2023

References

J. Brillhart et al., Factorizations of b^n +- 1. Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 2nd edition, 1985; and later supplements.

J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 109, p. 38, Ellipses, Paris 2008.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=1..14.

P. 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, Generalized repunit primes, Math. Comp., 61 (1993), 927-930.

H. Dubner, Generalized repunit primes, Math. Comp., 61 (1993), 927-930. [Annotated scanned copy]

H. Lifchitz, Mersenne and Fermat primes field

S. S. Wagstaff, Jr., The Cunningham Project

Eric Weisstein's World of Mathematics, Repunit

Mathematica

lst={}; Do[If[PrimeQ[(12^n-1)/11], Print[n]; AppendTo[lst, n]], {n, 10^5}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 21 2008 *)

Prog

(PARI) is(n)=ispseudoprime((12^n-1)/11) \\ Charles R Greathouse IV, Apr 29 2015

Crossrefs

Sequence in context: A235622 A235637 A028490 * A164061 A128363 A106047

Adjacent sequences: A004061 A004062 A004063 * A004065 A004066 A004067

Keyword

nonn,hard

Author

N. J. A. Sloane

Extensions

a(11) from Paul Bourdelais, Aug 03 2007

One more term from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 05 2008

a(13)=46889, discovered Sep 10 2008 by Paul Bourdelais, corresponds to a probable prime based on trial factoring to 10^13 and Fermat base 2 primality test. - Paul Bourdelais, Sep 11 2008

a(14)=769543 corresponds to a probable prime discovered by Paul Bourdelais, Dec 05 2014

Status

approved