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

Author

Jonathan Vos Post, Sep 12 2010

Keywords

• nonn
• look

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.

Examples

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

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.

Crossrefs

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

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