S000339


Reduced hypotenuses of right triangles in which the hypotenuse and one leg are triangular numbers.

4, 9, 16, 25, 25, 25, 25, 29, 34, 35, 36, 39, 49, 64, 65, 81, 100, 100, 100, 105, 108, 111, 121, 122, 122, 136, 144, 148, 149, 149, 156, 164, 164, 168, 169, 170, 177, 182, 194, 196, 220, 220, 225, 225, 256, 259, 279, 289, 290, 313, 318, 318, 318, 324, 339

1

S000339

A triangular number has the form n*(n+1)/2; by “reduced”, we mean that the number n is shown.

T. D. Noe, Plot of 100 terms

T. D. Noe, Table of 100 terms

Eric W. Weisstein, MathWorld: Triangular Number

(Mma) nn = 1000; t = {}; Do[If[IntegerQ[z = Sqrt[-a^2 (a + 1)^2 + b^2 (b + 1)^2]/2], AppendTo[t, {b, a, z}]], {a, nn}, {b, a+1, nn}]; t = Sort[t]; First /@ t

Cf. S000337, S000338, S000340.

nonn

T. D. Noe, Nov 13 2014

© Tony D Noe 2014-2015