A268603 Denominator of the side lengths (legs in ascending order) of the easiest Pythagorean Triangle (with smallest hypotenuse) according to the congruent numbers A003273.

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

Offset

1,1

Comments

Every three fractions x < y < z satisfy the Pythagorean equation x^2 + y^2 = z^2: (A268602(3*n-2)/a(3*n-2))^2 + (A268602(3*n-1)/a(3*n-1))^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*n-2)/a(3*n-2) * A268602(3*n-1)/a(3*n-1)).

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,tabf,more

Author

Martin Renner, Feb 08 2016

Extensions

a(14) corrected on Mar 14 2020

Status

approved