1,1

All such numbers k are prime.

Note that a(6) = 110503 corresponds to (36^110503 + 1)/37, which is only a probable prime with 171975 digits.

The primes corresponding to the terms of this sequence have 1 as their last digit and an even number as their next-to-last digit. -Iain Fox,Dec 08 2017

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.

Do[ p=Prime[n]; If[ PrimeQ[ (36^p + 1)/37 ], Print[p] ], {n, 1, 9592} ]

(PARI) is(n)=isprime((36^n+1)/37) \\Charles R Greathouse IV,Feb 17 2017

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.

Sequence in context:A042876A042878A165130*A261354A023292A100689

Adjacent sequences:A229142A229143A229144*A229146A229147A229148

hard,more,nonn

Robert Price,Sep 15 2013

a(6) = 110503 (posted by Lelio R. Paula on primenumbers.net) fromPaul Bourdelais,Dec 08 2017

a(7) fromPaul Bourdelais,Nov 03 2023

approved