A346134 The sum S of the maximum number of consecutive primes starting with 2 such that S <= prime(n)^2.

2, 5, 17, 41, 100, 160, 281, 328, 501, 791, 874, 1264, 1593, 1720, 2127, 2747, 3447, 3638, 4438, 4888, 5117, 6081, 6870, 7699, 9206, 10191, 10538, 11240, 11599, 12718, 15968, 16840, 18650, 19113, 22039, 22548, 24133, 26369, 27517, 29897, 31734, 32353, 36227, 36888

Offset: 1

Author

Gil Broussard, Jul 05 2021

Keywords

• nonn

Examples

			a(3) = 2+3+5+7 = 17 because 17 <= prime(3)^2 < 28 = 2+3+5+7+11.
a(4) = 2+3+5+7+11+13 = 41 because 41 <= prime(4)^2 < 58 = 2+3+5+7+11+13+17.
		

Crossrefs

Cf. A001248, A007504.

Programs

Mathematica

Table[k=1;While[(s=Sum[Prime@i,{i,++k}])Giorgos Kalogeropoulos, Jul 06 2021 *)

PARI

a(n) = my(s=0, p=2); while (s+p <= prime(n)^2, s += p; p = nextprime(p+1)); s; \\ Michel Marcus, Jul 05 2021

Python

from sympy import prime, nextprime
def a(n):
    p, s, lim = 1, 0, prime(n)**2
    while s <= lim: p = nextprime(p); s += p
    return s - p
print([a(n) for n in range(1, 51)]) # Michael S. Branicky, Jul 05 2021