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 A345707 #7 Jun 25 2021 02:36:35
%S A345707 2,5,11,13,19,41,47,67,89,149,211,331,433,677,859,1301
%N A345707 Primes prime(k) at which A345706(k) attains a record value.
%C A345707 The corresponding records values are 1, 2, 3, 6, 12, 20, 24, 58, 322, 414, 483, 527, 1065, 2597, 3181, 6022, ...
%e A345707 The first 6 terms of A345706 are 1, 1, 2, 2, 3 and 6. The record values, 1, 2, 3 and 6, occur at k = 1, 3, 5 and 6. The corresponding primes are prime(k) = 2, 5, 11 and 13, the first 4 terms of this sequence.
%t A345707 f[n_] := Module[{r = Product[Prime[j], {j, 1, n - 1}], p = Prime[n], k}, k = Max[1, Ceiling@Log[p, r]]; While[! PrimeQ[r*p^k + 1], k++]; k]; fm = 0; s = {}; Do[f1 = f[k]; If[f1 > fm, fm = f1; AppendTo[s, Prime[ k]]], {k, 1, 50}]; s
%Y A345707 Cf. A053341, A345706.
%K A345707 nonn,more
%O A345707 1,1
%A A345707 _Amiram Eldar_, Jun 24 2021