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%I #21 Feb 27 2024 02:44:21
%S 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,
%T 20,16,480,24,44,16,12,15,12,360,15,9,9,40,924,33,24,528,1104,14,168,
%U 14,24,20,28,72,33,33,76,40,1740,11,11,960,16,48,16,88,2244,32,92,24
%N Shortest other side of a Pythagorean triangle having n as length of one of the three sides.
%H Robert G. Wilson v, <a href="/A055525/b055525.txt">Table of n, a(n) for n = 3..10000</a>
%F From _Robert G. Wilson v_, Feb 23 2024: (Start)
%F sqrt(2*(n-1)) < a(n) < n^2/2.
%F If n = k*m, then a(n) <= k*a(m). (End)
%t 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 *)
%Y Cf. A009112, A046079, A046080, A046081, A054435, A054436, A055522, A055523, A055524, A055526, A055527.
%K nonn
%O 3,1
%A _Henry Bottomley_, May 22 2000
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