1,1

The definition implies that k must be a prime.

a(7) > 10^5.

Paul Bourdelais, A Generalized Repunit Conjecture.

John Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.

Harvey Dubner and Torbjörn Granlund, Primes of the Form (b^n+1)/(b+1), J. Integer Sequences, 3 (2000), #P00.2.7.

Henri 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.

Select[Prime[Range[10000]], PrimeQ[(20^# + 19^#)/39] &] (* corrected by Lyle Blosser, Dec 20 2025 *)

(PARI) isok(k) = my(x=(20^k + 19^k)/39); denominator(x)==1 && ispseudoprime(x); \\ Michel Marcus, Dec 20 2025

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

Sequence in context: A137017 A133833 A142260 * A016140 A138930 A106136

Adjacent sequences: A389261 A389262 A389263 * A389265 A389266 A389267

nonn,hard,more

Robert Price, Sep 27 2025

Name corrected by Lyle Blosser, Dec 20 2025

approved