A385064 Numbers k such that (31^k - 3^k)/28 is prime.

3, 23, 53, 661, 8923, 9721, 13807

Offset

1,1

Comments

The definition implies that k must be a prime.

a(8) > 10^5.

Links

Table of n, a(n) for n=1..7.

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.

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

Mathematica

Select[Prime[Range[10000]], PrimeQ[(31^# - 3^#)/28] &]

Crossrefs

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

Sequence in context: A031907 A181422 A082244 * A232193 A141047 A196538

Adjacent sequences: A385061 A385062 A385063 * A385065 A385066 A385067

Keyword

nonn,hard,more

Author

Robert Price, Jun 16 2025

Status

approved