A231100 Even legs of primitive Pythagorean triples (with multiplicity) sorted with respect to increasing hypotenuse.

4, 12, 8, 24, 20, 12, 40, 28, 60, 16, 56, 48, 36, 84, 80, 72, 20, 60, 112, 44, 88, 24, 144, 140, 132, 120, 52, 180, 104, 176, 168, 28, 84, 156, 140, 220, 60, 208, 120, 32, 96, 264, 260, 252, 160, 240, 68, 136, 224, 312, 308, 36, 204, 288, 180, 272, 76, 364, 252, 152, 352, 340, 228

Offset: 1

Author

K. G. Stier, Nov 03 2013

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 (increasing) even leg - that is, the terms go in the increasing order. [Corrected by Andrey Zabolotskiy, Oct 31 2019]

Only the even legs 'b' 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(13) = sqrt(A020882(13)^2-A180620(13)^2) = sqrt(85^2-77^2) = sqrt(1296) = 36.
		

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.

Crossrefs

Cf. A020882, A180620.

Formula

a(n) = sqrt(A020882(n)^2-A180620(n)^2).