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

3,1

Links

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

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)

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 *)

Crossrefs

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

Sequence in context: A138187 A105342 A323601 * A370574 A309046 A007568

Adjacent sequences: A055522 A055523 A055524 * A055526 A055527 A055528

Keyword

nonn

Author

Henry Bottomley, May 22 2000

Status

approved