A057173 Numbers n such that (7^n + 1)/8 is a prime.
3, 17, 23, 29, 47, 61, 1619, 18251, 106187, 201653, 1178033
Offset: 1
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
lst={};Do[p=(7^n+1)/8;If[PrimeQ[p], AppendTo[lst, n]], {n, 7!}];lst (* Vladimir Joseph Stephan Orlovsky, Sep 29 2008 *) -
PARI
isok(n) = (denominator(p=(7^n+1)/8)==1) && isprime(p); \\ Michel Marcus, Oct 30 2017
Extensions
a(9)=106187 is a probable prime based on Fermat primality testing and trial factoring to 2E13. - Paul Bourdelais, Apr 07 2008
a(10)=201653 is a probable prime discovered by Paul Bourdelais, Feb 17 2010
a(11)=1178033 corresponds to a probable prime discovered by Paul Bourdelais, Jan 11 2019
Comments