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

1,1

Comments

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

Links

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

Formula

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

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A254678 A165353 A048976 * A265816 A246717 A295706

Adjacent sequences: A088543 A088544 A088545 * A088547 A088548 A088549

Keyword

nonn

Author

Lekraj Beedassy, Nov 17 2003

Extensions

More terms from Ray Chandler, Nov 16 2003

Status

approved