A180620 Odd legs of primitive Pythagorean triples (with multiplicity) sorted with respect to increasing hypotenuse.

3, 5, 15, 7, 21, 35, 9, 45, 11, 63, 33, 55, 77, 13, 39, 65, 99, 91, 15, 117, 105, 143, 17, 51, 85, 119, 165, 19, 153, 57, 95, 195, 187, 133, 171, 21, 221, 105, 209, 255, 247, 23, 69, 115, 231, 161, 285, 273, 207, 25, 75, 323, 253, 175, 299, 225, 357, 27, 275, 345, 135, 189, 325

Offset

1,1

Comments

The primary key is the increasing length of the hypotenuse, A020882. If there is more than one solution with that hypotenuse, the (secondary) sorting key is the even leg.

Only the odd legs 'a' of reduced triangles with gcd(a,b,c)=1, a^2+b^2=c^2, a=q^2-p^2, b=2*p*q, c=q^2+p^2, gcd(p,q)=1 are listed.

Links

K. G. Stier, Table of n, a(n) for n = 1..1593

Michael Somos, Pythagorean Triple Table, Reduced integer right triangles, Feb 28, 1998.

Wikipedia, Pythagorean Triple.

Index entries related to Pythagorean Triples.

Example

a(1) = 3 because the only triangle with the least possible hypotenuse 5 has catheti 3 and 4.

Crossrefs

Cf. A046086, A046087, A020882, A081874, A231100.

Sequence in context: A270464 A058220 A100181 * A336882 A332382 A277323

Adjacent sequences: A180617 A180618 A180619 * A180621 A180622 A180623

Keyword

nonn,look

Author

Jonathan Vos Post, Sep 12 2010

Extensions

Comment on sorting added, more terms appended by R. J. Mathar, Oct 15 2010

Sequence's name and comments corrected by K. G. Stier, Nov 03 2013

Status

approved