A382391 Numbers k such that (23^k - 3^k)/20 is prime.

3, 7, 31, 47, 109, 151, 223, 463, 739, 6427, 17581, 30517

Offset: 1

Author

Robert Price, Mar 23 2025

Keywords

• nonn
• hard
• more

Comments

The definition implies that k must be a prime.

a(13) > 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. A062587, A062589, A127996, A127997, A128344, A204940, A217320, A225807, A229542, A375161, A375236, A377031.

Programs

Mathematica

Select[Prime[Range[10000]], PrimeQ[(23^# - 3^#)/20] &]