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

1,1

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

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

Crossrefs

Cf. A121727, A121728.

Sequence in context: A304026 A110641 A379042 * A072105 A350693 A364847

Adjacent sequences: A121726 A121727 A121728 * A121730 A121731 A121732

Keyword

nonn

Author

Lekraj Beedassy, Aug 17 2006

Extensions

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

Status

approved