

A268603


Denominator of the side lengths (legs in ascending order) of the easiest Pythagorean Triangle (with smallest hypotenuse) according to the congruent numbers A003273.


1



2, 3, 6, 1, 1, 1, 12, 5, 60, 323, 30, 9690, 3, 6, 6, 1, 2, 2, 1, 3, 3, 2, 1, 2, 35, 3, 105, 20748, 3485, 72306780
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OFFSET

1,1


COMMENTS

Every three fractions x < y < z satisfy the Pythagorean equation x^2 + y^2 = z^2: (A268602(3*n2)/a(3*n2))^2 + (A268602(3*n1)/a(3*n1))^2 = (A268602(3*n)/a(3*n))^2.
The area A = x*y/2 of these Pythagorean triangles is a congruent number: A003273(n) = (1/2) * A268602(3*n2)/a(3*n2) * A268602(3*n1)/a(3*n1)).


LINKS

Table of n, a(n) for n=1..30.
Eric Weisstein's World of Mathematics, Congruent Number.


EXAMPLE

The first congruent number is 5 and the associated right triangle with the side lengths x = 3/2, y = 20/3, z = 41/6 satisfies the Pythagorean equation (3/2)^2 + (20/3)^2 = (41/6)^2 and the area of this triangle equals 1/2*3/2*20/3 = 5.


CROSSREFS

Cf. A003273, A268602.
Sequence in context: A217100 A241293 A107409 * A226871 A178483 A133031
Adjacent sequences: A268600 A268601 A268602 * A268604 A268605 A268606


KEYWORD

nonn,frac,more,tabf


AUTHOR

Martin Renner, Feb 08 2016


STATUS

approved



