A353024 Largest k such that A007504(k) <= n^2.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 9, 10, 11, 11, 12, 13, 14, 14, 15, 16, 17, 17, 18, 19, 19, 20, 21, 21, 22, 23, 23, 24, 25, 25, 26, 27, 27, 28, 29, 30, 30, 31, 31, 32, 33, 33, 34, 35, 35, 36, 37, 37, 38, 39, 39, 40, 40, 41, 42, 42, 43, 44, 44, 45, 45, 46, 47, 47

Offset

1,3

Links

Table of n, a(n) for n=1..68.

Formula

a(n) = A337769(n) - 1.

a(n) ~ sqrt(2)*n/sqrt(log n). - Charles R Greathouse IV, Apr 18 2022

a(n) = A350174(n^2). - Kevin Ryde, Apr 19 2022

Prog

(Python)
from sympy import prime
def a(n):
    k = 1
    total = 0
    while True:
        total += prime(k)
        if total > n**2:
            break
        k += 1
    return k-1
(PARI) first(N)=my(v=vector(N), s, k, n=1, n2=1); forprime(p=2, , s+=p; k++; while(s>n2, v[n]=k-1; if(n++>N, return(v)); n2=n^2)) \\ Charles R Greathouse IV, Apr 18 2022
(PARI) a(n)=my(n2=n^2, s, k); forprime(p=2, , s+=p; k++; if(s>n2, return(k-1))) \\ Charles R Greathouse IV, Apr 18 2022

Crossrefs

Cf. A000290, A007504, A337769, A350174, A033997.

Sequence in context: A258632 A263283 A128635 * A100637 A081063 A081304

Adjacent sequences: A353021 A353022 A353023 * A353025 A353026 A353027

Keyword

nonn

Author

Joelle H. Kassir, Apr 17 2022

Status

approved