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 A268602 #37 Mar 06 2025 04:44:52 %S A268602 3,20,41,3,4,5,35,24,337,780,323,106921,8,21,65,4,15,17,3,40,41,7,12, %T A268602 25,33,140,4901,80155,41496,905141617,6,8,10,35,48,337,99,52780, %U A268602 48029801,5,12,13,720,8897,2566561,17,24,145,450660,777923,605170417321,1700,5301,1646021 %N A268602 Numerator of the side lengths (legs in ascending order) of the easiest Pythagorean Triangle (with smallest hypotenuse) according to the congruent numbers A003273. %C A268602 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. %C A268602 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)). %H A268602 Editors of OEIS, <a href="/A268602/a268602.txt">Discussion of A268602</a>, Apr 22 2023. %H A268602 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CongruentNumber.html">Congruent Number</a>. %e A268602 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 A268602 Cf. A003273, A268603. %K A268602 nonn,frac,tabf %O A268602 1,1 %A A268602 _Martin Renner_, Feb 08 2016 %E A268602 a(14) corrected on Mar 14 2020 %E A268602 More terms from _Jinyuan Wang_, Apr 22 2023