A005808 Numbers k such that (11^k - 1)/10 is prime.

17, 19, 73, 139, 907, 1907, 2029, 4801, 5153, 10867, 20161, 293831, 1868983

Offset: 1

Author

N. J. A. Sloane

Keywords

• hard
• more
• nonn

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.
• 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
• Henri & Renaud Lifchitz, PRP Records.
• S. S. Wagstaff, Jr., The Cunningham Project
• Eric Weisstein's World of Mathematics, Repunit.
• Index to primes in various ranges, form ((k+1)^n-1)/k

Programs

Mathematica

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

PARI

is(n)=ispseudoprime((11^n-1)/10) \\ Charles R Greathouse IV, Apr 29 2015

Extensions

a(11) = 20161 was found by Kamil Duszenko on Aug 15 2003. - Alexander Adamchuk, Feb 11 2007

a(12) = 293831 corresponds to a probable prime discovered by Paul Bourdelais with PFGW v3.3.1, Mar 08 2010

a(13) by Paul Bourdelais, Jun 01 2021