A381149 a(1) = 2, a(2) = 3; thereafter, a(n) = a(n-1) + sum of prior prime terms.

2, 3, 8, 13, 31, 80, 129, 178, 227, 503, 1282, 2061, 2840, 3619, 4398, 5177, 5956, 6735, 7514, 8293, 17365, 26437, 61946, 97455, 132964, 168473, 203982, 239491, 275000, 310509, 346018, 381527, 798563, 1215599, 1632635, 2049671, 2466707, 5350450, 8234193, 11117936

Offset: 1

Author

James C. McMahon, Feb 15 2025

Keywords

• nonn

Examples

			For n=5, a(5) = a(4) + sum of prior primes = 13 + (2 + 3 + 13) = 31, so that 13 is counted twice.
		

Links

• James C. McMahon, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A101135, A119746, A131093, A381150.

Programs

Mathematica

Nest[Append[#,#[[-1]]+Total[Select[#,PrimeQ]]]&,{2,3},38]

Python

from sympy import isprime
from itertools import count, islice
def agen(): # generator of terms
    yield from [2, 3]
    primesum, an = 5, 3
    while True:
        an += primesum
        if isprime(an): primesum += an
        yield an
print(list(islice(agen(), 40))) # Michael S. Branicky, Feb 19 2025