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 A355958 #11 Jul 21 2022 16:14:47
%S A355958 2,3,4,8,12,18,19,35,39,47,53,65,75,81,84,102,109,127,131,261,265,273,
%T A355958 283,305,323,329,350,450,456,462,492,522,562,660,664,784,904,922,1081,
%U A355958 1213,1258,1406,1443,1467,1549,1655,1772,1774,1786,1810,1901,1919,2024,2144,2161
%N A355958 Positions where primes occur in A104589.
%e A355958 The 1st prime in A104589 is 2, and its position is 2, so a(1) = 2.
%e A355958 The 2nd prime in A104589 is 5, and its position is 3, so a(2) = 3.
%e A355958 The 3rd prime in A104589 is 13, and its position is 4, so a(3) = 4.
%t A355958 s[1] = 1; s[n_] := s[n] = s[n - 1] + Sum[If[CompositeQ[s[k]], 0, s[k]], {k, 1, n - 1}]; Select[Range[2000], PrimeQ[s[#]] &] (* _Amiram Eldar_, Jul 21 2022 *)
%o A355958 (PARI) lista(nn) = my(last=1, s = 1, list = List()); for (n=2, nn, last += s; if (isprime(last), s += last; listput(list, n));); Vec(list);
%Y A355958 Cf. A104589, A355967.
%K A355958 nonn
%O A355958 1,1
%A A355958 _Michel Marcus_, Jul 21 2022