A121727 Hypotenuse of primitive Pythagorean triangles sorted on area (A024406), then on hypotenuse.

5, 13, 17, 25, 41, 29, 37, 61, 65, 85, 53, 113, 65, 101, 145, 73, 85, 89, 181, 145, 221, 97, 125, 109, 197, 265, 149, 313, 257, 173, 137, 365, 185, 157, 325, 421, 229, 169, 481, 205, 185, 193, 401, 269, 545, 293

Offset

1,1

Comments

Complete triple (X,Y,Z), with X>Y>Z is given by X=a(n),Y=A121728(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])):
R[.., 3]; # Robert Israel, Dec 30 2024

Prog

(PARI) v=vector(M=10^4); for(a=1, M, v[a] = []; fordiv(2*a, x, if(x<(y=2*a/x) && issquare(x^2+y^2, &z) && 1==gcd([x, y, z]), v[a] = concat(z, v[a])))); concat(v) /* Michael Somos, Dec 21 2016 */

Crossrefs

Cf. A024406, A121728, A121729.

Sequence in context: A094194 A088511 A089545 * A119321 A078900 A113482

Adjacent sequences: A121724 A121725 A121726 * A121728 A121729 A121730

Keyword

nonn

Author

Lekraj Beedassy, Aug 17 2006

Extensions

a(20)=145 corrected by Philippe Guglielmetti, Dec 14 2016

a(43)=401 inserted by Michael Somos, Dec 21 2016

Status

approved