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 A383039 #11 Apr 22 2025 15:42:05
%S A383039 7,1,17,31,97,241,647,1681,4417,11551,30257,79201,207367,542881,
%T A383039 1421297,3720991,9741697,25504081,66770567,174807601,457652257,
%U A383039 1198149151,3136795217,8212236481,21499914247,56287506241,147362604497,385800307231,1010038317217,2644314644401,6922905616007
%N A383039 Sum of the legs of the unique primitive Pythagorean triple (a,b,c) such that (a-b+c)/2 = A000032(n) and its long leg and hypotenuse are consecutive natural numbers.
%D A383039 Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2025.
%H A383039 Miguel-Ángel Pérez García-Ortega, <a href="/A383039/a383039.pdf">El Libro de las Ternas Pitagóricas</a>
%F A383039 a(n) = A382379(n,1) + A382379(n,2).
%F A383039 a(n) = 2*Lucas(n)^2 - 1.
%F A383039 a(n) = 2*A001254(n) - 1.
%e A383039 For n=3, the short leg is A382379(3,1) = 5 and the long leg is A382379(3,2) = 12 so the sum of the legs is then a(2) = 5 + 12 = 17.
%t A383039 a=Table[LucasL[n],{n,0,30}];Apply[Join,Map[{2#^2-1}&,a]]
%Y A383039 Cf. A000032, A382379, A382409, A382410, A001254.
%K A383039 nonn,easy
%O A383039 0,1
%A A383039 _Miguel-Ángel Pérez García-Ortega_, Apr 13 2025