A381018 a(n) is the number of primes in A000328 for r <= n.

1, 2, 3, 3, 3, 4, 5, 6, 6, 7, 7, 7, 7, 8, 9, 10, 10, 11, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 14, 15, 15, 15, 16, 16, 16, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 21, 21, 21, 22, 22, 22, 22, 22, 22, 23, 23, 23

Offset: 1

Author

Michel Marcus, Feb 12 2025

Keywords

• nonn

Comments

Number of Gauss circle primes for r <= n.

Links

• Thomas Ehrenborg, Gauss Circle Primes, arXiv:2502.06804 [math.GM], 2025. See Table 2 p. 4.

Crossrefs

Cf. A000328, A000720, A381017, A381020.

Programs

PARI

a(n) = sum(k=0, n, isprime(1 + 4*sum(j=0, k^2\4, k^2\(4*j+1) - k^2\(4*j+3))));

Python

from math import isqrt
from sympy import isprime
def A381018(n): return sum(1 for m in range(1,n+1) if isprime(1+(sum(isqrt(k*((m<<1)-k)) for k in range(1,m+1))<<2))) # Chai Wah Wu, Feb 13 2025