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 A383834 #18 Jul 13 2025 17:25:49
%S A383834 1,7,31,97,241,511,967,1681,2737,4231,6271,8977,12481,16927,22471,
%T A383834 29281,37537,47431,59167,72961,89041,107647,129031,153457,181201,
%U A383834 212551,247807,287281,331297,380191,434311,494017,559681,631687,710431,796321,889777,991231,1101127,1219921,1348081
%N A383834 Sum of the legs of the unique primitive Pythagorean triple whose inradius is A000217(n) and such that its long leg and its hypotenuse are consecutive natural numbers.
%D A383834 Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2025.
%H A383834 Miguel-Ángel Pérez García-Ortega, <a href="/A383834/a383834.pdf">El Libro de las Ternas Pitagóricas</a>
%F A383834 a(n) = 2*(A000217(n))^2 + 4*A000217(n) + 1.
%F A383834 a(n) = 6*A006007(n) + 1
%e A383834 For n=1, the short leg is A002061(1) = 3 and the long leg is A212135(2) = 4 so the sum of the legs is then a(1) = 3 + 4 = 7.
%t A383834 a=Table[(n(n+1))/2,{n,0,40}];Apply[Join,Map[{2#^2+4#+1}&,a]]
%Y A383834 Cf. A000217, A383833, A002061, A006007, A058919, A336535.
%K A383834 nonn,easy
%O A383834 0,2
%A A383834 _Miguel-Ángel Pérez García-Ortega_, May 11 2025