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

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

Offset: 1

Author

Paul Bourdelais, Dec 09 2021

Keywords

• nonn
• hard
• more

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).

Examples

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

Links

• Paul Bourdelais, A Generalized Repunit Conjecture

Crossrefs

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

Programs

Mathematica

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

PARI

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