A057180 Numbers n such that (14^n + 1)/15 is a prime.

7, 53, 503, 1229, 22637, 1091401, 1385203

Offset

1,1

Comments

Of the Repunit primes with base -21<=b<=21, base=-14 is the most "unlucky" with a normalized prime occurrence rate of 0.82247. The Generalized Repunit Conjecture (see link below) states that this will eventually improve and converge to Euler's Constant (~0.55). - Paul Bourdelais, Mar 10 2014 [updated Paul Bourdelais, Feb 08 2022]

Links

Table of n, a(n) for n=1..7.

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

Prog

(Prime95) PRP=1, 14, 1091401, 1, 0, 0, "15"

Crossrefs

Sequence in context: A142981 A350252 A120272 * A137612 A092802 A062207

Adjacent sequences: A057177 A057178 A057179 * A057181 A057182 A057183

Keyword

nonn

Author

N. J. A. Sloane, Sep 15 2000

Extensions

a(5) from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 05 2008

a(6)=1091401 is a probable prime discovered by Paul Bourdelais, Mar 10 2014

a(7) from Paul Bourdelais, Feb 08 2022

Status

approved