A355967 - OEIS

%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