A387473 Numbers k such that (31^k + 3^k)/34 is prime.

3, 5, 313, 677

Offset: 1

Author

Robert Price, Aug 30 2025

Keywords

• nonn
• hard
• more
• new

Comments

The definition implies that k must be a prime.

a(5) > 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.
• OEIS Wiki, Primes of the form (a^n+b^n)/(a+b) and (a^n-b^n)/(a-b)

Crossrefs

Cf. A057187, A057188, A062587, A062589, A127996, A127997, A128344, A204940, A217320, A225807, A228922, A229542, A375161, A375236, A377031, A377856.

Programs

Mathematica

Select[Prime[Range[10000]], PrimeQ[(31^# + 3^#)/34] &]