A185240 Numbers k such that (35^k + 1)/36 is prime.

11, 13, 79, 127, 503, 617, 709, 857, 1499, 3823, 135623, 280979

Offset

1,1

Comments

All terms are primes. a(11) > 10^5.

Links

Table of n, a(n) for n=1..12.

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, Repunit

Mathematica

Do[ p=Prime[n]; If[ PrimeQ[ (35^p + 1)/36 ], Print[p] ], {n, 1, 9592} ]

Prog

(PARI) is(n)=isprime((35^n+1)/36) \\ Charles R Greathouse IV, Feb 17 2017

Crossrefs

Cf. A000978 = numbers n such that (2^n + 1)/3 is prime. Cf. A007658, A057171, A057172, A057173, A057175, A001562, A057177, A057178, A057179, A057180, A057181, A057182, A057183, A057184, A057185, A057186, A057187, A057188, A057189, A057190, A057191, A071380, A071381, A071382. Cf. A084741, A084742, A065507, A126659, A126856.

Sequence in context: A186640 A226242 A116436 * A056446 A023317 A056436

Adjacent sequences: A185237 A185238 A185239 * A185241 A185242 A185243

Keyword

hard,more,nonn

Author

Robert Price, Aug 29 2013

Extensions

a(11)=135623 found as probable prime and added by Paul Bourdelais, Jul 05 2018

a(12) from Paul Bourdelais, Sep 13 2021

Status

approved