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A121728 Middle side (or long leg) of primitive Pythagorean triangle corresponding to hypotenuse A121727.

%I A121728 #10 Dec 30 2024 02:17:18
%S A121728 4,12,15,24,40,21,35,60,63,84,45,112,56,99,144,55,77,80,180,143,220,
%T A121728 72,117,91,195,264,140,312,255,165,105,364,176,132,323,420,221,120,
%U A121728 480,187,153,168,399,260,544,285
%N A121728 Middle side (or long leg) of primitive Pythagorean triangle corresponding to hypotenuse A121727.
%C A121728 Complete triple (X,Y,Z), with X>Y>Z, is given by X=A121727(n),Y=a(n),Z=A121729(n).
%H A121728 Robert Israel, <a href="/A121728/b121728.txt">Table of n, a(n) for n = 1..10000</a>
%p A121728 N:= 100000: # for triples with area <= N
%p A121728 R:= NULL:
%p A121728 for n from 1 while (2*n+1)*(n+1)*n <= N do
%p A121728   for m from n+1 by 2 while (m^2 - n^2)*m*n <= N do
%p A121728     if igcd(m,n) = 1 then
%p A121728       R:= R, [m^2-n^2,2*m*n,m^2+n^2,(m^2-n^2)*m*n]
%p A121728     fi
%p A121728 od od:
%p A121728 R:= sort(R, (s,t) -> s[4] < t[4] or (s[4] = t[4] and s[3] < t[3])):
%p A121728 seq(max(t[1],t[2]),t=R); # _Robert Israel_, Dec 30 2024
%Y A121728 Cf. A121727, A121729.
%K A121728 nonn
%O A121728 1,1
%A A121728 _Lekraj Beedassy_, Aug 17 2006
%E A121728 a(43)=399 inserted by _Ray Chandler_, Jun 26 2017