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 A379506 #13 Jul 13 2025 19:35:28
%S A379506 3,4,5,13,84,85,183,16744,16745,33673,566935464,566935465,1133904603,
%T A379506 642869824352293804,642869824352293805,1285739649838492213,
%U A379506 826563223583404284483387832630818684,826563223583404284483387832630818685
%N A379506 Sequence of primitive Pythagorean triples beginning with the triple (3,4,5), with each subsequent triple having as its inradius the semiperimeter of the previous triple, and with the long leg and the hypotenuse of each triple being consecutive natural numbers.
%C A379506 The only Pythagorean triple whose inradius is equal to r and such that its long leg and its hypotenuse are consecutive is (2r+1,2r^2+2r,2r^2+2r+1).
%H A379506 Miguel-Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz, and José Miguel Blanco Casado, <a href="/A379506/a379506.pdf">El Libro de las Ternas Pitagóricas</a>, Preprint, 2024.
%e A379506 Triples begin:
%e A379506 3, 4, 5;
%e A379506 13, 84, 85;
%e A379506 183, 16744, 16745;
%e A379506 33673, 566935464, 566935465;
%t A379506 {a0,b0,c0}={3,4,5};f[n_]:= Module[{fn0=a0+b0+c0+1,fn1=((a0+b0+c0+1)^2+1)/2},Do[{fn0,fn1}={2fn1+fn0,((2fn1+fn0)^2+1)/2},{n}];fn0];t[n_]:={f[n-1],(f[n-1]^2-1)/2,(f[n 1]^2+1)/2};ternas={a0,b0,c0};For[i=1,i<=6,i++,ternas=Join[ternas,t[i]]];ternas
%Y A379506 Cf. A002065 (short leg), A378395, A365577, A378963
%K A379506 nonn,tabf
%O A379506 1,1
%A A379506 _Miguel-Ángel Pérez García-Ortega_, Dec 23 2024