A088544 Scale factor by which primitive Pythagorean triangle {x=A088509(n), y=A088510(n), z=A088511(n)} needs be enlarged in order to circumscribe the smallest integral square having a side on the hypotenuse.

37, 229, 409, 793, 1261, 2041, 1789, 4381, 5233, 4069, 8317, 6073, 14449, 7969, 12181, 9997, 11041, 23473, 14089, 24457, 17341, 36181, 20773, 53461, 29341, 44269, 28009, 38509, 76297, 35869, 44257, 74209, 42841, 105769, 50137, 65701, 53209

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

Cf. A088509, A088510, A088511, A063011.

Sequence in context: A230006 A284987 A133958 * A051463 A275750 A142445

Adjacent sequences: A088541 A088542 A088543 * A088545 A088546 A088547

Keyword

nonn

Author

Lekraj Beedassy, Nov 17 2003

Extensions

More terms from Max Alekseyev, May 30 2009

Status

approved