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
Keywords
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.
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
Comments