cp's OEIS Frontend

A381330 Numbers that are the sum of a prime and the square of a prime in more than one way.

%I A381330 #17 Feb 21 2025 11:12:25
%S A381330 11,27,28,32,38,51,52,54,56,62,66,68,72,78,80,86,92,96,98,108,110,116,
%T A381330 122,126,128,132,134,138,140,146,150,152,156,158,162,164,171,172,174,
%U A381330 176,180,182,186,188,192,198,200,204,206,210,212,216,218,222,224,228
%N A381330 Numbers that are the sum of a prime and the square of a prime in more than one way.
%C A381330 Subsequence of A081053. Most terms are even. The odd terms are 11, 27, 51, 171, 363, 843, 1371, 1851 and must be of the form 2+p^2=4+q for primes p, q. In particular, the odd terms are exactly A049002(n)+4 for n>1.
%H A381330 Chai Wah Wu, <a href="/A381330/b381330.txt">Table of n, a(n) for n = 1..10000</a>
%e A381330 11 is a term since 11 = 2^2+7  = 3^2+2.
%e A381330 27 is a term since 27 = 2^2+23 = 5^2+2.
%e A381330 28 is a term since 28 = 3^2+19 = 5^2+3.
%e A381330 32 is a term since 32 = 3^2+23 = 5^2+7.
%o A381330 (Python)
%o A381330 from math import isqrt
%o A381330 from itertools import count, islice
%o A381330 from sympy import isprime, primerange
%o A381330 def A381330_gen(startvalue=1): # generator of terms >= startvalue
%o A381330     for n in count(max(startvalue,1)):
%o A381330         c = 0
%o A381330         for p in primerange(isqrt(n)+1):
%o A381330             if isprime(n-p**2):
%o A381330                 c += 1
%o A381330             if c>1:
%o A381330                 yield n
%o A381330                 break
%o A381330 A381330_list = list(islice(A381330_gen(),30))
%o A381330 (PARI) isok(k) = my(nb=0); forprime(p=2, sqrtint(k), if (isprime(k-p^2), nb++);); nb > 1; \\ _Michel Marcus_, Feb 21 2025
%Y A381330 Cf. A081053, A049002.
%K A381330 nonn
%O A381330 1,1
%A A381330 _Chai Wah Wu_, Feb 20 2025