cp's OEIS Frontend

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

%I A381333 #9 Feb 21 2025 06:09:01
%S A381333 6,11,56,176,188,362,398,668,1448,1448,1592,2390,3372,3632,4532,6342,
%T A381333 6342,6368,6368,10632,12920,12920,12942,19502,23168,25038,25038,25038,
%U A381333 25472,32238,32238,39800,39800,39800,53360,64998,72740,72740,72740,81542,82880,82880
%N A381333 Smallest integer that is the sum of a prime and the square of a prime in n or more ways.
%C A381333 Subsequence of A081053. All terms are even except for a(2) = 11.
%e A381333 a(1) = 6 as 6 = 2 + 2^2.
%e A381333 a(2) = 11 as 11 = 7 + 2^2 = 2 + 3^2.
%e A381333 a(3) = 56 as 56 = 47 + 3^2 = 31 + 5^2 = 7 + 7^2.
%e A381333 a(4) = 176 as 176 = 167 + 3^2 = 151 + 5^2 = 127 + 7^2 = 7 + 13^2.
%e A381333 a(5) = 188 as 188 = 179 + 3^2 = 163 + 5^2 = 139 + 7^2 = 67 + 11^2 = 19 + 13^2.
%e A381333 a(6) = 362 as 362 = 353 + 3^2 = 337 + 5^2 = 313 + 7^2 = 241 + 11^2 = 193 + 13^2 = 73 + 17^2.
%o A381333 (Python)
%o A381333 from itertools import count
%o A381333 from math import isqrt
%o A381333 from sympy import isprime, primerange
%o A381333 def A381333(n):
%o A381333     for m in count(1):
%o A381333         c = 0
%o A381333         for p in primerange(isqrt(m)+1):
%o A381333             if isprime(m-p**2):
%o A381333                 c += 1
%o A381333             if c>=n:
%o A381333                 return m
%o A381333 (PARI) f(k) = my(nb=0); forprime(p=2, sqrtint(k), if (isprime(k-p^2), nb++);); nb;
%o A381333 a(n) = my(k=1); while (f(k) < n, k++); k; \\ _Michel Marcus_, Feb 21 2025
%Y A381333 Cf. A001172, A081053, A381330.
%K A381333 nonn
%O A381333 1,1
%A A381333 _Chai Wah Wu_, Feb 20 2025