A057173 Numbers k such that (7^k + 1)/8 is a prime.

3, 17, 23, 29, 47, 61, 1619, 18251, 106187, 201653, 1178033, 1321757, 1827773, 3417779

Offset

1,1

Comments

(7^1619+1)/8, a 1368-digit number, has been certified prime with Primo. - Rick L. Shepherd, May 19 2002

Links

Table of n, a(n) for n=1..14.

Paul Bourdelais, A Generalized Repunit Conjecture.

John Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.

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

Henri Lifchitz, Mersenne and Fermat primes field.

Eric Weisstein's World of Mathematics, Repunit.

Mathematica

lst={}; Do[p=(7^n+1)/8; If[PrimeQ[p], AppendTo[lst, n]], {n, 7!}]; lst (* Vladimir Joseph Stephan Orlovsky, Sep 29 2008 *)

Prog

(PARI) isok(n) = (denominator(p=(7^n+1)/8)==1) && isprime(p); \\ Michel Marcus, Oct 30 2017

Crossrefs

Sequence in context: A019380 A296937 A126692 * A109371 A272176 A082372

Adjacent sequences: A057170 A057171 A057172 * A057174 A057175 A057176

Keyword

nonn,more,hard

Author

N. J. A. Sloane, Sep 15 2000

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

a(12)=1321757 by Paul Bourdelais, Oct 13 2025

a(13)=1827773 by Paul Bourdelais, Oct 27 2025

a(14)=3417779 by Paul Bourdelais, Nov 17 2025

Status

approved