A057172 Numbers n such that (6^n + 1)/7 is a prime.

3, 11, 31, 43, 47, 59, 107, 811, 2819, 4817, 9601, 33581, 38447, 41341, 131891, 196337, 1313371

Offset

1,1

Comments

a(15), a(16) and a(17) correspond to probable primes.

Links

Table of n, a(n) for n=1..17.

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 and T. Granlund, Primes of the Form (b^n+1)/(b+1), J. Integer Sequences, 3 (2000), #P00.2.7.

H. Lifchitz, Mersenne and Fermat primes field

Eric Weisstein's World of Mathematics, Repunit

Mathematica

Select[Range[5000], PrimeQ[(6^# + 1) / 7] &] (* Vincenzo Librandi, Oct 29 2017 *)

Prog

(PARI) isok(n) = (denominator(p=(6^n+1)/7)==1) && isprime(p); \\ Michel Marcus, Oct 29 2017

Crossrefs

Sequence in context: A018781 A119215 A266970 * A277167 A277049 A261148

Adjacent sequences: A057169 A057170 A057171 * A057173 A057174 A057175

Keyword

nonn,more

Author

N. J. A. Sloane, Sep 15 2000

Extensions

a(12) was discovered by Kamil Duszenko, Jul 15 2003

a(13) was discovered by Henri Lifchitz, Sep 15 2007

a(14) was discovered by Paul Bourdelais, Oct 01 2007

a(15) was discovered by Paul Bourdelais, Feb 01 2010

a(16) was discovered by Paul Bourdelais, Feb 19 2010

a(17) was discovered by Paul Bourdelais, Jan 28 2019

Status

approved