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

1,1

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.

Links

Table of n, a(n) for n=1..66.

Example

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.

Sequence in context: A232487 A243936 A257263 * A028760 A028807 A242994

Adjacent sequences: A133999 A134000 A134001 * A134003 A134004 A134005

Keyword

nonn

Author

John W. Layman, Oct 01 2007

Status

approved