A004063 Numbers k such that (7^k - 1)/6 is prime. (Formerly M3836)

5, 13, 131, 149, 1699, 14221, 35201, 126037, 371669, 1264699

Offset

1,1

Comments

Base-7 repunit primes. - Paul Bourdelais, Aug 31 2007

Among repunits with bases from -11 to 11, base-7 repunits have the lowest relative rate of occurrence of primes so far. - Paul Bourdelais, Feb 23 2010

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.

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..10.

Paul 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

For[n = 1, n <= 20000, n++, If[PrimeQ[(7^n - 1)/6 ], Print[n]]] (* Sam Handler (sam_5_5_5_0(AT)yahoo.com), Aug 09 2006 *)

Prog

(Prime95) PRP=1, 7, 1264699, -1, 0, 0, "6"
(PARI) is(n)=isprime((7^n - 1)/6) \\ Charles R Greathouse IV, Apr 28 2015

Crossrefs

Sequence in context: A155175 A155185 A213129 * A005764 A358922 A305643

Adjacent sequences: A004060 A004061 A004062 * A004064 A004065 A004066

Keyword

nonn,hard

Author

N. J. A. Sloane

Extensions

a(6) from Robert G. Wilson v, Apr 09 2005

a(7) is a probable prime from Paul Bourdelais, Aug 31 2007

a(8) discovered Sep 17 2008 by Paul Bourdelais & Eric Purohit - it is a probable prime based on trial factoring to 2.5*10^13 and Fermat base 2 primality test. - Paul Bourdelais, Sep 18 2008

a(9) is a probable prime discovered by Paul Bourdelais, Feb 23 2010

a(10) is a probable prime discovered by Paul Bourdelais, Jan 06 2014

Status

approved