A055525 Shortest other side of a Pythagorean triangle having n as length of one of the three sides.

4, 3, 3, 8, 24, 6, 12, 6, 60, 5, 5, 48, 8, 12, 8, 24, 180, 12, 20, 120, 264, 7, 7, 10, 36, 21, 20, 16, 480, 24, 44, 16, 12, 15, 12, 360, 15, 9, 9, 40, 924, 33, 24, 528, 1104, 14, 168, 14, 24, 20, 28, 72, 33, 33, 76, 40, 1740, 11, 11, 960, 16, 48, 16, 88, 2244, 32, 92, 24

Offset: 3

Author

Henry Bottomley, May 22 2000

Keywords

• nonn

Links

• Robert G. Wilson v, Table of n, a(n) for n = 3..10000

Crossrefs

Cf. A009112, A046079, A046080, A046081, A054435, A054436, A055522, A055523, A055524, A055526, A055527.

Programs

Mathematica

a[n_] := Block[{a, c, k = 1, n2 = n^2}, While[ If[ k > n, !IntegerQ[c = Sqrt[n2 + k^2]], !IntegerQ[c = Sqrt[n2 + k^2]] && !IntegerQ[a = Sqrt[n2 - k^2]]], k++; If[k == n, k++]]; If[ IntegerQ@ c, k, Sqrt[n2 - a^2]]]; (* Robert G. Wilson v, Feb 23 2024 *)

Formula

From Robert G. Wilson v, Feb 23 2024: (Start)

sqrt(2*(n-1)) < a(n) < n^2/2.

If n = k*m, then a(n) <= k*a(m). (End)