A229524 Numbers k such that (38^k + 1)/39 is prime.

5, 167, 1063, 1597, 2749, 3373, 13691, 83891, 131591

Offset: 1

Author

Robert Price, Sep 25 2013

Keywords

• hard
• more
• nonn

Comments

All terms are primes. a(9) > 10^5.

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.

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, A084741, A084742, A065507, A126659, A126856, A185240, A229145.

Programs

Mathematica

Do[ p=Prime[n]; If[ PrimeQ[ (38^p + 1)/39 ], Print[p] ], {n, 1, 9592} ]

PARI

is(n)=ispseudoprime((38^n+1)/39) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

a(9)=131591 corresponds to a probable prime discovered by Paul Bourdelais, Jul 03 2018