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

1,1

Comments

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

Links

Table of n, a(n) for n=1..42.

Example

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.

Prog

(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
(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

Crossrefs

Cf. A001172, A081053, A381330.

Sequence in context: A341943 A271119 A271299 * A381334 A177197 A177162

Adjacent sequences: A381330 A381331 A381332 * A381334 A381338 A381339

Keyword

nonn

Author

Chai Wah Wu, Feb 20 2025

Status

approved