cp's OEIS Frontend

A121729 Shortest side (or short leg) of primitive Pythagorean triangle corresponding to hypotenuse A121727.

%I A121729 #9 Dec 30 2024 02:17:29
%S A121729 3,5,8,7,9,20,12,11,16,13,28,15,33,20,17,48,36,39,19,24,21,65,44,60,
%T A121729 28,23,51,25,32,52,88,27,57,85,36,29,60,119,31,84,104,95,40,69,33,68
%N A121729 Shortest side (or short leg) of primitive Pythagorean triangle corresponding to hypotenuse A121727.
%C A121729 The complete triple (X,Y,Z), with X>Y>Z, is given by X=A121727(n),Y=A121728(n),Z=a(n).
%H A121729 Robert Israel, <a href="/A121729/b121729.txt">Table of n, a(n) for n = 1..10000</a>
%p A121729 N:= 100000: # for triples with area <= N
%p A121729 R:= NULL:
%p A121729 for n from 1 while (2*n+1)*(n+1)*n <= N do
%p A121729   for m from n+1 by 2 while (m^2 - n^2)*m*n <= N do
%p A121729     if igcd(m, n) = 1 then
%p A121729       R:= R, [m^2-n^2, 2*m*n, m^2+n^2, (m^2-n^2)*m*n]
%p A121729     fi
%p A121729 od od:
%p A121729 R:= sort(R, (s, t) -> s[4] < t[4] or (s[4] = t[4] and s[3] < t[3])):
%p A121729 seq(min(t[1], t[2]), t=R); # _Robert Israel_, Dec 30 2024
%Y A121729 Cf. A121727, A121728.
%K A121729 nonn
%O A121729 1,1
%A A121729 _Lekraj Beedassy_, Aug 17 2006
%E A121729 a(43)=40 inserted by _Ray Chandler_, Jun 26 2017