A381333 Smallest integer that is the sum of a prime and the square of a prime in n or more ways.

6, 11, 56, 176, 188, 362, 398, 668, 1448, 1448, 1592, 2390, 3372, 3632, 4532, 6342, 6342, 6368, 6368, 10632, 12920, 12920, 12942, 19502, 23168, 25038, 25038, 25038, 25472, 32238, 32238, 39800, 39800, 39800, 53360, 64998, 72740, 72740, 72740, 81542, 82880, 82880

Offset: 1

Author

Chai Wah Wu, Feb 20 2025

Keywords

• nonn

Comments

Subsequence of A081053. All terms are even except for a(2) = 11.

Examples

			a(1) = 6 as 6 = 2 + 2^2.
a(2) = 11 as 11 = 7 + 2^2 = 2 + 3^2.
a(3) = 56 as 56 = 47 + 3^2 = 31 + 5^2 = 7 + 7^2.
a(4) = 176 as 176 = 167 + 3^2 = 151 + 5^2 = 127 + 7^2 = 7 + 13^2.
a(5) = 188 as 188 = 179 + 3^2 = 163 + 5^2 = 139 + 7^2 = 67 + 11^2 = 19 + 13^2.
a(6) = 362 as 362 = 353 + 3^2 = 337 + 5^2 = 313 + 7^2 = 241 + 11^2 = 193 + 13^2 = 73 + 17^2.
		

Crossrefs

Cf. A001172, A081053, A381330.

Programs

PARI

f(k) = my(nb=0); forprime(p=2, sqrtint(k), if (isprime(k-p^2), nb++);); nb;
a(n) = my(k=1); while (f(k) < n, k++); k; \\ Michel Marcus, Feb 21 2025

Python

from itertools import count
from math import isqrt
from sympy import isprime, primerange
def A381333(n):
    for m in count(1):
        c = 0
        for p in primerange(isqrt(m)+1):
            if isprime(m-p**2):
                c += 1
            if c>=n:
                return m