A395474 Numbers k such that (32^k - 5^k)/27 is prime.

2, 5, 23, 79, 977, 1489, 1621, 10007, 11677, 32797, 39901, 43051, 60383, 86981

Offset

1,1

Comments

The definition implies that k must be a prime.

a(15) > 10^5.

Links

Table of n, a(n) for n=1..14.

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

OEIS Wiki, Primes of the form (a^n+b^n)/(a+b) and (a^n-b^n)/(a-b)

Eric Weisstein's World of Mathematics, Repunit.

Mathematica

Select[Prime[Range[10000]], PrimeQ[(32^# - 5^#)/27] &]

Crossrefs

Cf. A062587, A062589, A127996, A127997, A128344, A204940, A217320, A225807, A229542, A375161, A375236, A377031.

Sequence in context: A173396 A023186 A023188 * A106858 A380852 A376156

Adjacent sequences: A395471 A395472 A395473 * A395475 A395476 A395477

Keyword

nonn,hard,more,changed

Author

Robert Price, Apr 24 2026

Status

approved