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 A382114 #27 May 05 2025 22:35:12
%S A382114 6,6,15,66,435,3655,35245,369370,4094091,47292675,564261621,
%T A382114 6911763951,86538608325,1103803048701,14305266650521,187980068232586,
%U A382114 2500329761730811,33615543537222571,456277456908296101,6246438370759741771,86175353796214314061,1197196443861278161861,16738118900567747790121,235379797036403711485951
%N A382114 Semiperimeter of the unique primitive Pythagorean triple whose inradius is A000108(n) and such that its long leg and its hypotenuse are consecutive natural numbers.
%D A382114 Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2025.
%H A382114 Miguel-Ángel Pérez García-Ortega, <a href="/A382114/a382114.pdf">El Libro de las Ternas Pitagóricas</a>
%F A382114 a(n) = (A383251(n,1) + A383251(n,2) + A383251(n,3))/2.
%F A382114 a(n) = (A000108(n) + 1)*(2*A000108(n) + 1).
%e A382114 For n=2, the short leg is A383251(2,1) = 3, the long leg is A383251(2,2) = 4 and the hypotenuse is A383251(2,3) = 5 so the semiperimeter is then a(2) = (3 + 4 + 5)/2 = 6.
%t A382114 a=Table[(2n)!/(n!(n+1)!),{n,0,23}];Apply[Join,Map[{(#+1)(2#+1)}&,a]]
%Y A382114 Cf. A000108, A383251, A381483.
%K A382114 nonn,easy
%O A382114 0,1
%A A382114 _Miguel-Ángel Pérez García-Ortega_, Apr 22 2025