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 A345705 #7 Jun 25 2021 02:36:22
%S A345705 13,29,35,47,53,71,95,133,263,275,485,529,773,1009,1261,1559,2711,
%T A345705 3767,4009,5275,7613,8645,10295,11605,21311,27755,29927,40565,44519,
%U A345705 67135,67849,75335,83333,105469,107185,153557,164365,383705,405623,420341,443105
%N A345705 Numbers k such that (3^ord(3/2, k) - 2^ord(3/2, k))/k is a prime, where ord(3/2, k) is the multiplicative order of 3/2 (mod k).
%C A345705 Numbers k such that gcd(k, 6) = 1 and if m is the least positive integer such that k divides 3^m - 2^m, then (3^m - 2^m)/k is a prime number.
%C A345705 The corresponding primes are 5, 71, 19, 2002867877, 29927, 29, 7, 5, ...
%H A345705 Wikipedia, <a href="http://en.wikipedia.org/wiki/Multiplicative_order">Multiplicative order</a>.
%H A345705 Wikipedia, <a href="https://en.wikipedia.org/wiki/Zsigmondy%27s_theorem">Zsigmondy's theorem</a>.
%F A345705 13 is a term since ord(3/2, 13) = 4 and (3^4 - 2^4)/13 = 5 is a prime number.
%t A345705 ord[n_] := Module[{k = 1}, While[! Divisible[PowerMod[3, k, n] - PowerMod[2, k, n], n], k++]; k]; f[k_] := 3^k - 2^k; Select[Range[1000], CoprimeQ[6, #] && PrimeQ[f[ord[#]]/#] &]
%Y A345705 Cf. A297362, A297363, A320383.
%K A345705 nonn
%O A345705 1,1
%A A345705 _Amiram Eldar_, Jun 24 2021