A108708 - OEIS

%I #19 Jan 02 2022 01:13:42

%S 0,0,0,0,4,0,0,0,0,8,0,0,12,0,12,0,15,0,0,16,0,0,0,0,24,24,0,0,21,24,

%T 0,0,0,30,28,0,35,0,36,32,40,0,0,0,36,0,0,0,0,48,45,48,45,0,44,0,0,42,

%U 0,48,60,0,0,0,63,0,0,60,0,56,0,0,55,70,72,0,0,72,0,64,0,80,0,0,84,0,63,0

%N Maximum side length in Pythagorean triangles with hypotenuse n.

%H David A. Corneth, <a href="/A108708/b108708.txt">Table of n, a(n) for n = 1..10000</a>

%e a(5) is 4 as the maximum side (other than the hypotenuse) a right triangle with integer sides and hypotenuse 5 can have.

%t f[n_] := Block[{k = n - 1, m = Sqrt[n/2]}, While[k > m && !IntegerQ[Sqrt[n^2 - k^2]], k-- ]; If[k <= m, 0, k]]; Table[ f[n], {n, 90}] (* _Robert G. Wilson v_, Jun 21 2005 *)

%o (PARI) first(n) = {my(lh = List(), res = vector(n)); for(u = 2, sqrtint(n), for(v = 1, u, if (u^2+v^2 > n, break); if ((gcd(u, v) == 1) && (0 != (u-v)%2), for (i = 1, n, if (i*(u^2+v^2) > n, break); listput(lh, i*(u^2+v^2)); res[i*(u^2+v^2)] = max(res[i*(u^2+v^2)], max(i*(u^2 - v^2), i*2*u*v)); ); ); ); ); for(i = 1, n, if(res[i] == oo, res[i] = 0)); res } \\ _David A. Corneth_, Apr 10 2021, adapted from A009000

%Y Cf. A083025, A046083, A046084, A009000, A009003, A108707.

%Y A046080 gives the number of Pythagorean triangles with hypotenuse n.

%K nonn

%O 1,5

%A _Sébastien Dumortier_, Jun 20 2005

%E More terms from _Robert G. Wilson v_, Jun 21 2005