A134002 Positive integers n such that n(n+5)=a(a+5)+b(b+5) is solvable in positive integers.

5, 10, 11, 13, 15, 16, 20, 23, 24, 25, 30, 31, 33, 35, 36, 37, 38, 40, 42, 45, 46, 47, 49, 50, 55, 57, 60, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 73, 75, 76, 80, 81, 84, 85, 86, 88, 89, 90, 92, 95, 98, 99, 100, 101, 102, 105, 108, 110, 111, 112, 114, 115, 118, 120, 124, 125

Offset: 1

Author

John W. Layman, Oct 01 2007

Keywords

• nonn

Comments

Conjecture. If n a positive integer not a term of this sequence, then n^2+(n+5)^2 is prime. (This has been verified up to n=500.) Examples. For n=1,2,3,4,6,7, n^2+(n+5)^2 is 37, 53,73, 97, 157 and 193, each of which is prime. See A134003 for the complement of this sequence.

Examples

			5(5+5)=50=14+36=2(2+5)+4(4+5), so 5 is a term of the sequence.
		

Crossrefs

Cf. A012132, A027861, A134003.