This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A350036 #12 Dec 10 2021 11:35:27
%S A350036 3,5,701,829,1031,1033,7229,19463,370421
%N A350036 Numbers k such that (81^k + 1)/82 is prime.
%C A350036 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).
%H A350036 Paul Bourdelais, <a href="https://listserv.nodak.edu/cgi-bin/wa.exe?A2=NMBRTHRY;417ab0d6.0906">A Generalized Repunit Conjecture</a>
%e A350036 3 is a term since (81^3 + 1)/82 = 6481 is a prime.
%t A350036 Do[ If[ PrimeQ[ (81^n+1)/82], Print[n]], {n, 0, 1000000}]
%o A350036 (PARI) is(n)=isprime((81^n+1)/82)
%Y A350036 Cf. A309533, A309532, A237052, A229145, A057191, A057182, A057175.
%K A350036 nonn,hard,more
%O A350036 1,1
%A A350036 _Paul Bourdelais_, Dec 09 2021