A350036 Numbers k such that (81^k + 1)/82 is prime.

3, 5, 701, 829, 1031, 1033, 7229, 19463, 370421

Offset

1,1

Comments

These are the Repunits in base -81. Since 81=3^4, factors will be of the form p=8nk+1. (Negative) bases that are powers of small numbers appear to have a higher frequency of primes than Repunits in other bases. The best linear fit for this base is currently 0.29918 which is much lower (better) than the conjectured 0.56145948 (see link to conjecture).

Links

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

Paul Bourdelais, A Generalized Repunit Conjecture

Example

3 is a term since (81^3 + 1)/82 = 6481 is a prime.

Mathematica

Do[ If[ PrimeQ[ (81^n+1)/82], Print[n]], {n, 0, 1000000}]

Prog

(PARI) is(n)=isprime((81^n+1)/82)

Crossrefs

Cf. A309533, A309532, A237052, A229145, A057191, A057182, A057175.

Sequence in context: A369097 A320939 A002427 * A136134 A119497 A298094

Adjacent sequences: A350033 A350034 A350035 * A350037 A350038 A350039

Keyword

nonn,hard,more

Author

Paul Bourdelais, Dec 09 2021

Status

approved