This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A268603 #27 Mar 06 2025 08:17:32 %S A268603 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, %T A268603 20748,3485,72306780 %N A268603 Denominator of the side lengths (legs in ascending order) of the easiest Pythagorean Triangle (with smallest hypotenuse) according to the congruent numbers A003273. %C A268603 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. %C A268603 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)). %H A268603 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CongruentNumber.html">Congruent Number</a>. %e A268603 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. %Y A268603 Cf. A003273, A268602. %K A268603 nonn,frac,tabf,more %O A268603 1,1 %A A268603 _Martin Renner_, Feb 08 2016 %E A268603 a(14) corrected on Mar 14 2020