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

4, 12, 15, 24, 40, 21, 35, 60, 63, 84, 45, 112, 56, 99, 144, 55, 77, 80, 180, 143, 220, 72, 117, 91, 195, 264, 140, 312, 255, 165, 105, 364, 176, 132, 323, 420, 221, 120, 480, 187, 153, 168, 399, 260, 544, 285

Offset: 1

Author

Lekraj Beedassy, Aug 17 2006

Keywords

• nonn

Comments

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

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A121727, A121729.

Programs

Maple

N:= 100000: # for triples with area <= N
R:= NULL:
for n from 1 while (2*n+1)*(n+1)*n <= N do
  for m from n+1 by 2 while (m^2 - n^2)*m*n <= N do
    if igcd(m,n) = 1 then
      R:= R, [m^2-n^2,2*m*n,m^2+n^2,(m^2-n^2)*m*n]
    fi
od od:
R:= sort(R, (s,t) -> s[4] < t[4] or (s[4] = t[4] and s[3] < t[3])):
seq(max(t[1],t[2]),t=R); # Robert Israel, Dec 30 2024

Extensions

a(43)=399 inserted by Ray Chandler, Jun 26 2017