A121728 - OEIS

%I #10 Dec 30 2024 02:17:18

%S 4,12,15,24,40,21,35,60,63,84,45,112,56,99,144,55,77,80,180,143,220,

%T 72,117,91,195,264,140,312,255,165,105,364,176,132,323,420,221,120,

%U 480,187,153,168,399,260,544,285

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

%C Complete triple (X,Y,Z), with X>Y>Z, is given by X=A121727(n),Y=a(n),Z=A121729(n).

%H Robert Israel, <a href="/A121728/b121728.txt">Table of n, a(n) for n = 1..10000</a>

%p N:= 100000: # for triples with area <= N

%p R:= NULL:

%p for n from 1 while (2*n+1)*(n+1)*n <= N do

%p   for m from n+1 by 2 while (m^2 - n^2)*m*n <= N do

%p     if igcd(m,n) = 1 then

%p       R:= R, [m^2-n^2,2*m*n,m^2+n^2,(m^2-n^2)*m*n]

%p     fi

%p od od:

%p R:= sort(R, (s,t) -> s[4] < t[4] or (s[4] = t[4] and s[3] < t[3])):

%p seq(max(t[1],t[2]),t=R); # _Robert Israel_, Dec 30 2024

%Y Cf. A121727, A121729.

%K nonn

%O 1,1

%A _Lekraj Beedassy_, Aug 17 2006

%E a(43)=399 inserted by _Ray Chandler_, Jun 26 2017