

A004064


Numbers n such that (12^n  1)/11 is prime.
(Formerly M0744)


13



2, 3, 5, 19, 97, 109, 317, 353, 701, 9739, 14951, 37573, 46889, 769543
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


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), 927930.
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^n1)/11], Print[n]; AppendTo[lst, n]], {n, 10^5}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 21 2008 *)


PROG

(PARI) is(n)=ispseudoprime((12^n1)/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



