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 A379509 #8 Jan 17 2025 17:05:58
%S A379509 7,127,3527,115199,3886471,131868799,4478743367,152140105727,
%T A379509 5168253960967,175568314524799,5964153390518471,202605640846963199,
%U A379509 6882627599758753927,233806732543181952127,7942546277657462785607,269812766700752532479999,9165691521506791484696071,311363698964290393026435199
%N A379509 Sum of the legs of the unique primitive Pythagorean triple whose inradius is A002315(n) and such that its long leg and its hypotenuse are consecutive natural numbers.
%C A379509 For all n: a(n) == 7 (mod 8).
%D A379509 Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2024.
%H A379509 Miguel-Ángel Pérez García-Ortega, <a href="/A379509/a379509.pdf">El Libro de las Ternas Pitagóricas</a>
%F A379509 a(n) = A377725(n,1) + A377725(n,2).
%e A379509 For n=2, the short leg is A377725(2,1) = 15 the long leg is A377725(2,2) = 112 so the semiperimeter is then a(2) = 15 + 112 = 127.
%t A379509 s[n_]:=s[n]=Module[{r},r=((1+Sqrt[2])^(2n+1)-(Sqrt[2]-1)^(2n+1))/2;{2r^2+4r+1}];sumas={};Do[semis=Join[sumas,FullSimplify[s[n]]],{n,0,17}];sumas
%Y A379509 Cf. A002315, A377025, A378386, A378380.
%K A379509 nonn,easy
%O A379509 0,1
%A A379509 _Miguel-Ángel Pérez García-Ortega_, Dec 23 2024