

A268602


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


1



3, 20, 41, 3, 4, 5, 35, 24, 337, 780, 323, 106921, 8, 63, 65, 4, 15, 17, 3, 40, 41, 7, 12, 25, 33, 140, 4901, 80155, 41496, 905141617
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Every three fractions x < y < z satisfy the Pythagorean equation x^2 + y^2 = z^2: (a(3*n2)/A268603(3*n2))^2 + (a(3*n1)/A268603(3*n1))^2 = (a(3*n)/A268603(3*n))^2.
The area A = x*y/2 of these Pythagorean triangles is a congruent number: A003273(n) = (1/2) * a(3*n2)/A268603(3*n2) * a(3*n1)/A268603(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, A268603.
Sequence in context: A254501 A031106 A248818 * A267055 A296252 A211068
Adjacent sequences: A268599 A268600 A268601 * A268603 A268604 A268605


KEYWORD

nonn,frac,more,tabf


AUTHOR

Martin Renner, Feb 08 2016


STATUS

approved



