A381149 Contribution to the OEIS

 A381149

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

+40
0

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

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OFFSET

1,1

LINKS

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

EXAMPLE

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

MATHEMATICA

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

PROG

(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

CROSSREFS

Cf. A101135, A119746, A131093, A381150.

KEYWORD

nonn,new

AUTHOR

James C. McMahon, Feb 15 2025

STATUS

approved

This sequence is similar to my other sequence submitted at the same time, A381150. However, I think A381150 is more interesting because of the terms that repeat and also how it cycles between positive and negative terms. Link to prior post: https://jamesmacmath.blogspot.com/2025/02/a-sequence-with-competing-sums-of-prior.html