A263015 Integers n such that A007504(n) is the sum of 2 nonzero squares.

1, 2, 3, 4, 6, 7, 9, 11, 12, 14, 15, 21, 25, 29, 35, 55, 58, 59, 64, 71, 85, 89, 93, 94, 95, 100, 101, 102, 108, 112, 114, 116, 122, 124, 130, 131, 133, 135, 141, 146, 147, 151, 159, 162, 165, 170, 171, 172, 177, 178, 183, 190, 192, 193, 194, 204, 205, 206

Offset: 1

Author

Altug Alkan, Nov 27 2015

Keywords

• nonn

Comments

Integers n such that sum of the first n primes is the sum of 2 nonzero squares.

Initial values of corresponding sum of first n primes are 2, 5, 10, 17, 41, 58, 100, 160, 197 and 281.

Examples

			a(3) = 3 because 2 + 3 + 5 = 3^2 + 1^2.
a(5) = 6 because 2 + 3 + 5 + 7 + 11 + 13 = 5^2 + 4^2.
a(6) = 7 because 2 + 3 + 5 + 7 + 11 + 13 + 17 = 7^2 + 3^2.
		

Crossrefs

Cf. A000404, A007504.

Programs

PARI

a(n) = sum(k=1, n, prime(k));
is(n) = { for( i=1, #n=factor(n)~%4, n[1, i]==3 && n[2, i]%2 && return); n && ( vecmin(n[1, ])==1 || (n[1, 1]==2 && n[2, 1]%2)) }
for(n=1, 1e3, if(is((a(n))), print1(n, ", ")))