A355967 Indices of the primes that occur in A104589.

1, 3, 6, 25, 104, 634, 1236, 22613, 103409, 929044, 6298419, 80396036, 843325558, 5843115733, 24428345613, 515211289906, 4021634909249, 77930896716918, 387592118891917, 53467625139656294, 258820291307490689, 2600667638804262010, 29899374277934530878

Offset: 1

Author

Michel Marcus, Jul 21 2022

Keywords

• nonn

Examples

			The primes in A104589 are 2, 5, 13, 97, ... with prime indices 1, 3, 6, 25, ...
		

Crossrefs

Cf. A000040, A000720, A104589, A355958.

Programs

Mathematica

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 *)

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);

Python

from sympy import isprime, primepi
from itertools import islice
def A355967_gen(): # generator of terms
    a, b = 1, 1
    while True:
        a += b
        if isprime(a):
            b += a
            yield primepi(a)
A355967_list = list(islice(A355967_gen(),14)) # Chai Wah Wu, Jun 03 2024

Extensions

a(14)-a(20) from Amiram Eldar, Jul 21 2022

a(21)-a(23) from Chai Wah Wu, Jun 03 2024