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%I #25 Jun 03 2024 08:53:12
%S 1,3,6,25,104,634,1236,22613,103409,929044,6298419,80396036,843325558,
%T 5843115733,24428345613,515211289906,4021634909249,77930896716918,
%U 387592118891917,53467625139656294,258820291307490689,2600667638804262010,29899374277934530878
%N Indices of the primes that occur in A104589.
%e The primes in A104589 are 2, 5, 13, 97, ... with prime indices 1, 3, 6, 25, ...
%t s[1] = 1; s[n_] := s[n] = s[n - 1] + Sum[If[CompositeQ[s[k]], 0, s[k]], {k, 1, n - 1}]; PrimePi[Select[s /@ Range[200], PrimeQ[#] &]] (* _Amiram Eldar_, Jul 21 2022 *)
%o (PARI) lista(nn) = my(last=1, s = 1, list = List()); for (n=2, nn, last += s; if (isprime(last), s += last; listput(list, primepi(last)));); Vec(list);
%o (Python)
%o from sympy import isprime, primepi
%o from itertools import islice
%o def A355967_gen(): # generator of terms
%o a, b = 1, 1
%o while True:
%o a += b
%o if isprime(a):
%o b += a
%o yield primepi(a)
%o A355967_list = list(islice(A355967_gen(),14)) # _Chai Wah Wu_, Jun 03 2024
%Y Cf. A000040, A000720, A104589, A355958.
%K nonn
%O 1,2
%A _Michel Marcus_, Jul 21 2022
%E a(14)-a(20) from _Amiram Eldar_, Jul 21 2022
%E a(21)-a(23) from _Chai Wah Wu_, Jun 03 2024