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

Author

N. J. A. Sloane, Sep 15 2000

Keywords

• nonn
• more

Comments

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

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 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

Programs

Mathematica

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

PARI

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

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