cp's OEIS Frontend

A378963 Sequence of primitive Pythagorean triples beginning with the triple (3,4,5), with each subsequent triple having as its inradius the short leg of the previous triple, and with the long leg and the hypotenuse of each triple being consecutive natural numbers.

%I A378963 #8 Jul 13 2025 19:35:42
%S A378963 3,4,5,7,24,25,15,112,113,31,480,481,63,1984,1985,127,8064,8065,255,
%T A378963 32512,32513,511,130560,130561,1023,523264,523265,2047,2095104,
%U A378963 2095105,4095,8384512,8384513,8191,33546240,33546241,16383,134201344,134201345
%N A378963 Sequence of primitive Pythagorean triples beginning with the triple (3,4,5), with each subsequent triple having as its inradius the short leg of the previous triple, and with the long leg and the hypotenuse of each triple being consecutive natural numbers.
%C A378963 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).
%D A378963 Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz, and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2024.
%e A378963 Triples begin:
%e A378963   3, 4, 5;
%e A378963   7, 24, 25;
%e A378963   15, 112, 113;
%e A378963   31, 480, 481;
%t A378963 a=Table[2^(n+1)-1,{n,1,13}];Apply[Join,Map[{#,(#^2-1)/2,(#^2+1)/2}&,a]]
%Y A378963 Cf. A000225 (short leg), A092440 (hypotenuse), A378395, A365577.
%K A378963 nonn,tabf
%O A378963 1,1
%A A378963 _Miguel-Ángel Pérez García-Ortega_, Dec 12 2024