A076600 a(n) = smallest k > n such that n^2 + k^2 is a square, or 0 if no such k exists.

1, 0, 0, 4, 0, 12, 8, 24, 15, 12, 24, 60, 16, 84, 48, 20, 30, 144, 24, 180, 21, 28, 120, 264, 32, 60, 168, 36, 45, 420, 40, 480, 60, 44, 288, 84, 48, 684, 360, 52, 42, 840, 56, 924, 117, 60, 528, 1104, 55, 168, 120, 68, 165, 1404, 72, 132, 90, 76, 840, 1740, 63, 1860

Offset: 0

Author

Zak Seidov, Oct 21 2002

Keywords

• easy
• nonn

Examples

			a(3)=4 because 3^2 + 4^2 = 5^2; a(17)=144 because 17^2 + 144^2 = 145^2.
		

Links

• Ivan Neretin, Table of n, a(n) for n = 0..10000

Programs

Mathematica

f[ n_ ] := Block[ {k = n + 1}, While[ ! IntegerQ[ Sqrt[ n^2 + k^2 ] ], k++ ]; k ]; Join[ {1, 0, 0, 4, 0}, Table[ f[ n ], {n, 5, 61} ] ]

PARI

a(n)=for(m=n+1,n^2\2+1,if(issquare(m^2+n^2),return(m)));0 /* Michael Somos, Mar 03 2004 */

Extensions

Edited by Robert G. Wilson v, Oct 23 2002