A005808 Numbers k such that (11^k - 1)/10 is prime. (Formerly M5032)

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

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.

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

Table of n, a(n) for n=1..13.

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

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 *)

Prog

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

Crossrefs

Sequence in context: A232882 A232878 A226681 * A180559 A272478 A028489

Adjacent sequences: A005805 A005806 A005807 * A005809 A005810 A005811

Keyword

hard,more,nonn

Author

N. J. A. Sloane

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

Status

approved