A397847 Numbers k such that (47^k + 4^k)/51 is prime.

53, 139, 853, 8179

Offset

1,1

Comments

The definition implies that k must be a prime.

a(5) > 10^5.

Links

Table of n, a(n) for n=1..4.

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

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.

Mathematica

Select[Prime[Range[10000]], PrimeQ[(47^# + 5^#)/51] &]

Crossrefs

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

Sequence in context: A239721 A391663 A142259 * A161611 A251076 A142043

Adjacent sequences: A397838 A397840 A397843 * A397851 A397852 A397855

Keyword

nonn,hard,more,new

Author

Robert Price, Jul 12 2026

Status

approved