A057182 Numbers n such that (16^n + 1)/17 is a prime.

3, 5, 7, 23, 37, 89, 149, 173, 251, 307, 317, 30197, 1025393

Offset: 1

Author

N. J. A. Sloane, Sep 15 2000

Keywords

• hard
• more
• nonn

Links

• 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 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, Ferrier's Prime

Crossrefs

Subsequence of A195439. [Arkadiusz Wesolowski, Dec 18 2011]

Programs

Mathematica

m = 16; Select[Range[0, 10^3], PrimeQ[(m^# + 1)/(m + 1)] & ] (* Robert Price, Oct 15 2018 *)

Prime95

PRP=1,2,4101572,1,0,0,"17"

Extensions

a(12) from Robert G. Wilson v, Apr 11 2005

a(13) gives a probable prime discovered by Paul Bourdelais, Aug 20 2014