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

1,1

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 (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.

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.

Formula

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

Example

a(13) = sqrt(A020882(13)^2-A180620(13)^2) = sqrt(85^2-77^2) = sqrt(1296) = 36.

Crossrefs

Cf. A020882, A180620.

Sequence in context: A252984 A084415 A156681 * A229179 A273172 A307853

Adjacent sequences: A231097 A231098 A231099 * A231101 A231102 A231103

Keyword

nonn,look

Author

K. G. Stier, Nov 03 2013

Status

approved