A004064 Numbers k such that (12^k - 1)/11 is prime.
2, 3, 5, 19, 97, 109, 317, 353, 701, 9739, 14951, 37573, 46889, 769543
Offset: 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.
- Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See p. 236.
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Links
- 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
Programs
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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 *) -
PARI
is(n)=ispseudoprime((12^n-1)/11) \\ Charles R Greathouse IV, Apr 29 2015
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
Comments