

A088546


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


17



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
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OFFSET

1,1


COMMENTS

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


LINKS



FORMULA



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]]& (* JeanFrançois Alcover, Mar 05 2020 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



