Pairs of numbers x > y > 0 such that x^2 + y^2 is a square, x is as small as possible, and x/y is unique.

4, 3, 12, 5, 15, 8, 21, 20, 24, 7, 35, 12, 40, 9, 45, 28, 55, 48, 56, 33, 60, 11, 63, 16, 72, 65, 77, 36, 80, 39, 84, 13, 91, 60, 99, 20, 105, 88, 112, 15, 117, 44, 120, 119, 132, 85, 140, 51, 143, 24, 144, 17, 153, 104, 156, 133, 165, 52, 168, 95, 171, 140, 176

1

All pairs are ralatively prime. Note that the numbers x are not strictly increasing. The first such pair of pairs is (420,29) and (420,341). In the sequences S000992 to S000995 we look at increasing the exponent of x and y from 2 to 3, 5, 7, and 9.

T. D. Noe, Plot of 1000 pairs

T. D. Noe, Table of 1000 pairs

(Mma) mx = 200; s2 = {}; t2 = {}; Do[If[IntegerQ[Sqrt[a^2 + b^2]] && ! MemberQ[s2, a/b], AppendTo[s2, a/b]; AppendTo[t2, {a, b}]], {a, 0, mx}, {b, a}]; t2

nonn,nice

T. D. Noe, Apr 06 2017