A231604 Numbers n such that (42^n + 1)/43 is prime.

3, 709, 1637, 17911, 127609, 172663

Offset

1,1

Comments

The first 5 terms are primes.

Links

Table of n, a(n) for n=1..6.

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

P. Bourdelais, A Generalized Repunit Conjecture

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[ (42^p + 1)/43 ], Print[p] ], {n, 1, 9592} ]

Prog

(PARI) is(n)=ispseudoprime((42^n+1)/43) \\ Charles R Greathouse IV, Feb 20 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, A084741, A084742, A065507, A126659, A126856, A185240, A229145, A229524, A230036, A229663.

Sequence in context: A203496 A308323 A276455 * A306961 A059120 A300947

Adjacent sequences: A231601 A231602 A231603 * A231605 A231606 A231607

Keyword

hard,more,nonn

Author

Robert Price, Nov 11 2013

Extensions

a(5)=127609 corresponds to a probable prime discovered by Paul Bourdelais, Jul 02 2018

a(6)=172663 corresponds to a probable prime discovered by Paul Bourdelais, Jul 29 2019

Status

approved