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

1,1

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

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

Crossrefs

Cf. A121727, A121729.

Sequence in context: A081872 A120097 A088510 * A324786 A032823 A224785

Adjacent sequences: A121725 A121726 A121727 * A121729 A121730 A121731

Keyword

nonn

Author

Lekraj Beedassy, Aug 17 2006

Extensions

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

Status

approved