A061409 For each y >= 1 there are only finitely many values of x >= 1 such that x-y and x+y are both positive squares; list all such pairs (x,y) ordered by values of y; sequence gives x values.

5, 10, 17, 26, 13, 37, 50, 20, 65, 82, 29, 101, 122, 25, 40, 145, 170, 53, 197, 34, 226, 68, 257, 290, 45, 85, 325, 362, 41, 104, 401, 58, 442, 125, 485, 530, 52, 73, 148, 577, 626, 173, 677, 90, 730, 65, 200, 785, 842, 61, 109, 229, 901, 962

Offset: 0

Author

Jason Earls, May 01 2001

Keywords

• nonn

Examples

			Pairs are [5, 4], [10, 6], [17, 8], [26, 10], [13, 12], [37, 12], [50, 14], ... For example, 5-4 = 1^2, 5+4 = 3^2.
		

References

• Donald D. Spencer, Computers in Number Theory, Computer Science Press, Rockville MD, 1982, pp. 130-131.

Links

• Robert Israel, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A061408, A060829, A060830.

Programs

Maple

seq(op(sort(map(k -> (k^2 + (y/2/k)^2), select(t -> t^2 < y/2, convert(numtheory:-divisors(y/2),list))))),y=2..100,2); # Robert Israel, Dec 10 2017

Formula

The solutions are given by x = r^2 + 2*r*k + 2*k^2, y = 2*k*(k+r) with r >= 1, k >= 1. - N. J. A. Sloane, May 02 2001

Extensions

Definition clarified by Robert Israel, Dec 10 2017