|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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]]& (* Jean-François Alcover, Mar 05 2020 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|