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 A379508 #15 Jul 13 2025 17:36:49
%S A379508 1,97,3361,114241,3880897,131836321,4478554081,152139002497,
%T A379508 5168247530881,175568277047521,5964153172084897,202605639573839041,
%U A379508 6882627592338442561,233806732499933208097,7942546277405390632801,269812766699283348307201,9165691521498228451812097,311363698964240484013304161
%N A379508 Sum of the legs of the unique primitive Pythagorean triple (a,b,c) such that (a-b+c)/2 is A002315(n) and such that its long leg and its hypotenuse are consecutive natural numbers.
%H A379508 Miguel-Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, <a href="/A379508/a379508.pdf">El Libro de las Ternas Pitagóricas</a>, preprint, 2024.
%F A379508 a(n) = A377726(n,1) + A377726(n,2).
%e A379508 For n=2, the short leg is A377726(2,1) = 13 and the long leg is A377725(2,2) = 84 so the semiperimeter is then a(2) = 13 + 84 = 97.
%t A379508 s[n_]:=s[n]=Module[{ra},ra=((1+Sqrt[2])^(2n+1)-(Sqrt[2]-1)^(2n+1))/2;{2ra^2-1}];sumas={};Do[sumas=Join[semis,FullSimplify[s[n]]],{n,0,17}];sumas
%Y A379508 Cf. A002315, A377016, A377017, A377726, A378965, A378965.
%K A379508 nonn,easy
%O A379508 0,2
%A A379508 _Miguel-Ángel Pérez García-Ortega_, Dec 23 2024