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

3, 5, 8, 7, 9, 20, 12, 11, 16, 13, 28, 15, 33, 20, 17, 48, 36, 39, 19, 24, 21, 65, 44, 60, 28, 23, 51, 25, 32, 52, 88, 27, 57, 85, 36, 29, 60, 119, 31, 84, 104, 95, 40, 69, 33, 68

Offset: 1

Author

Lekraj Beedassy, Aug 17 2006

Keywords

• nonn

Comments

The complete triple (X,Y,Z), with X>Y>Z, is given by X=A121727(n),Y=A121728(n),Z=a(n).

Links

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

Crossrefs

Cf. A121727, A121728.

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(min(t[1], t[2]), t=R); # Robert Israel, Dec 30 2024

Extensions

a(43)=40 inserted by Ray Chandler, Jun 26 2017