A088546 Square root of sum of legs of primitive Pythagorean triangles having legs that add up to a square, sorted on hypotenuse.

7, 17, 23, 31, 47, 41, 49, 71, 73, 79, 89, 97, 113, 103, 119, 119, 127, 137, 151, 161, 161, 167, 191, 199, 193, 217, 217, 233, 223, 241, 263, 271, 257, 239, 281, 287, 287, 313, 289, 329, 329, 343, 311, 353, 367, 337, 359, 383, 409, 391, 401, 391, 433, 439, 463

Offset: 1

Author

Lekraj Beedassy, Nov 17 2003

Keywords

• nonn

Comments

Numbers whose square is the sum of the legs of primitive Pythagorean triangles with hypotenuse A088319(n).

Examples

			31 is in the sequence because it is associated with the primitive Pythagorean triangle (400,561,689) where 400+561=31^2.
		

Links

• Ray Chandler, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A088319, A088515, A088516, A089545-A089552, A089554-A089558.

Programs

Mathematica

terms = 1000; jmax = 100; kmax = 200;
Reap[Do[If[CoprimeQ[j, k], e = j^2 - j k + k^2/2; f = j k; If[e > f, Sow[{e^2 + f^2, Abs[j^2 - k^2/2]}]]], {j, 1, jmax}, {k, 2, kmax, 2}]][[2, 1]] // Sort // #[[;; terms, 2]]& (* Jean-François Alcover, Mar 05 2020 *)

Formula

a(n) = abs(j^2 - k^2/2), where j=A088515(n), k=A088516(n).

a(n) = sqrt(A089552(n)).

Extensions

More terms from Ray Chandler, Nov 16 2003