A055527 - OEIS

%I #23 Feb 16 2024 10:12:23

%S 4,3,12,8,24,6,12,24,60,5,84,48,8,12,144,24,180,15,20,120,264,7,60,

%T 168,36,21,420,16,480,24,44,288,12,15,684,360,52,9,840,40,924,33,24,

%U 528,1104,14,168,120,68,39,1404,72,48,33,76,840,1740,11,1860,960,16,48,72

%N Shortest other leg of a Pythagorean triangle with n as length of a leg.

%C From _Alex Ratushnyak_, Mar 30 2014: (Start)

%C Least positive k such that n^2 + k^2 is a square.

%C For odd n, a(n) <= 4*triangular((n-1)/2), because n^2 + (4 * triangular((n-1)/2))^2 = ((n^2+1)/2) ^ 2, which is a perfect square since n is odd.

%C For n = 4*k+2, a(n) <= 8*triangular(k), because (4k+2)^2 + (4*k*(k+1))^2 = (4*k^2 + 4*k + 2)^2. (End)

%H T. D. Noe, <a href="/A055527/b055527.txt">Table of n, a(n) for n = 3..1000</a>

%F a(n) = sqrt(A055526(n)^2-n^2) = 2*A054436/n.

%t Table[k = 1; While[! IntegerQ[Sqrt[n^2 + k^2]], k++]; k, {n, 3, 100}] (* _T. D. Noe_, Apr 02 2014 *)

%Y Cf. A000290, A000217, A009112, A046079, A046080, A046081, A054435, A054436, A055522, A055523, A055524, A055525, A055526.

%Y See A082183 for a similar sequence involving triangular numbers.

%K nonn

%O 3,1

%A _Henry Bottomley_, May 22 2000