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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
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
Sequence in context: A254678 A165353 A048976 * A265816 A246717 A295706
KEYWORD
nonn
AUTHOR
Lekraj Beedassy, Nov 17 2003
EXTENSIONS
More terms from Ray Chandler, Nov 16 2003
STATUS
approved

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Last modified June 13 17:01 EDT 2024. Contains 373391 sequences. (Running on oeis4.)