A384972 Numbers k such that (25^k - 3^k)/22 is prime.

3, 5, 43, 709, 1151, 3323, 3643, 4637, 21661

Offset

1,1

Comments

The definition implies that k must be a prime.

a(10) > 10^5.

Links

Table of n, a(n) for n=1..9.

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[(25^# - 3^#)/22] &]

Crossrefs

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

Sequence in context: A386169 A386056 A199345 * A062633 A240559 A361904

Adjacent sequences: A384969 A384970 A384971 * A384973 A384974 A384975

Keyword

nonn,hard,more

Author

Robert Price, Jun 13 2025

Status

approved