A134002 - OEIS

%I #3 Mar 30 2012 17:37:54

%S 5,10,11,13,15,16,20,23,24,25,30,31,33,35,36,37,38,40,42,45,46,47,49,

%T 50,55,57,60,61,62,63,64,65,67,68,69,70,71,73,75,76,80,81,84,85,86,88,

%U 89,90,92,95,98,99,100,101,102,105,108,110,111,112,114,115,118,120,124,125

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

%C 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.

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

%Y Cf. A012132, A027861, A134003.

%K nonn

%O 1,1

%A _John W. Layman_, Oct 01 2007