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A355967 Indices of the primes that occur in A104589.

%I A355967 #25 Jun 03 2024 08:53:12
%S A355967 1,3,6,25,104,634,1236,22613,103409,929044,6298419,80396036,843325558,
%T A355967 5843115733,24428345613,515211289906,4021634909249,77930896716918,
%U A355967 387592118891917,53467625139656294,258820291307490689,2600667638804262010,29899374277934530878
%N A355967 Indices of the primes that occur in A104589.
%e A355967 The primes in A104589 are 2, 5, 13, 97, ... with prime indices 1, 3, 6, 25, ...
%t A355967 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 A355967 (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 A355967 (Python)
%o A355967 from sympy import isprime, primepi
%o A355967 from itertools import islice
%o A355967 def A355967_gen(): # generator of terms
%o A355967     a, b = 1, 1
%o A355967     while True:
%o A355967         a += b
%o A355967         if isprime(a):
%o A355967             b += a
%o A355967             yield primepi(a)
%o A355967 A355967_list = list(islice(A355967_gen(),14)) # _Chai Wah Wu_, Jun 03 2024
%Y A355967 Cf. A000040, A000720, A104589, A355958.
%K A355967 nonn
%O A355967 1,2
%A A355967 _Michel Marcus_, Jul 21 2022
%E A355967 a(14)-a(20) from _Amiram Eldar_, Jul 21 2022
%E A355967 a(21)-a(23) from _Chai Wah Wu_, Jun 03 2024