A268602 Numerator of the side lengths (legs in ascending order) of the easiest Pythagorean Triangle (with smallest hypotenuse) according to the congruent numbers A003273.

3, 20, 41, 3, 4, 5, 35, 24, 337, 780, 323, 106921, 8, 21, 65, 4, 15, 17, 3, 40, 41, 7, 12, 25, 33, 140, 4901, 80155, 41496, 905141617, 6, 8, 10, 35, 48, 337, 99, 52780, 48029801, 5, 12, 13, 720, 8897, 2566561, 17, 24, 145, 450660, 777923, 605170417321, 1700, 5301, 1646021

Offset

1,1

Comments

Every three fractions x < y < z satisfy the Pythagorean equation x^2 + y^2 = z^2: (a(3*n-2)/A268603(3*n-2))^2 + (a(3*n-1)/A268603(3*n-1))^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*n-2)/A268603(3*n-2) * a(3*n-1)/A268603(3*n-1)).

Links

Table of n, a(n) for n=1..54.

Editors of OEIS, Discussion of A268602, Apr 22 2023

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: A031106 A337478 A248818 * A344890 A072472 A267055

Adjacent sequences: A268599 A268600 A268601 * A268603 A268604 A268605

Keyword

nonn,frac,tabf

Author

Martin Renner, Feb 08 2016

Extensions

a(14) corrected on Mar 14 2020

More terms from Jinyuan Wang, Apr 22 2023

Status

approved