OFFSET
1,1
COMMENTS
Such an inscribed square has side x*y*z = A063011(n).
Also the radius squared of the Conway circle of a primitive Pythagorean triangle, sorted on product of sides. - Frank M Jackson, Nov 04 2023
REFERENCES
J. D. E. Konhauser et al., Which Way Did The Bicycle Go?, Problem 21, "The Square on the Hypotenuse", pp. 7; 79-80, Dolciani Math. Exp. No. 18, MAA, 1996.
LINKS
Frank M Jackson, Table of n, a(n) for n = 1..10000
Eric W. Weisstein, MathWorld: Conway circle.
Wikipedia, Conway circle theorem.
FORMULA
a(n) = x*y + z^2.
a(n) = s^2 + r^2, where s is the semiperimeter and r is the inradius of triangle (x, y, z).
MATHEMATICA
lst={}; k=25; Do[If[GCD[m, n]==1&&OddQ[m+n], AppendTo[lst, {2m*n(m^4-n^4), m^2(m+n)^2+n^2(m-n)^2}]], {m, 1, k}, {n, 1, m}]; lst=Sort@lst; Table[lst[[n]][[2]], {n, 1, 100}] (* Frank M Jackson, Nov 04 2023 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Lekraj Beedassy, Nov 17 2003
EXTENSIONS
More terms from Max Alekseyev, May 30 2009
STATUS
approved