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A367573 Long legs of the only primitive Pythagorean triple whose inradius is the n-th prime and whose short leg is an odd number.

%I A367573 #15 Jul 14 2025 18:01:30
%S A367573 12,24,60,112,264,364,612,760,1104,1740,1984,2812,3444,3784,4512,5724,
%T A367573 7080,7564,9112,10224,10804,12640,13944,16020,19012,20604,21424,23112,
%U A367573 23980,25764,32512,34584,37812,38920,44700,45904,49612,53464,56112,60204,64440
%N A367573 Long legs of the only primitive Pythagorean triple whose inradius is the n-th prime and whose short leg is an odd number.
%C A367573 See Ejercicio 2.7. of García-Ortega.
%H A367573 Miguel-Ángel Pérez García-Ortega, <a href="/A367573/a367573.pdf">Capítulo 2. Inradio, El Libro de las Ternas Pitagóricas</a>.
%F A367573 a(n) = 2*p^2 + 2*p where p is prime(n).
%e A367573 Triangles begin
%e A367573    5,  12,  13;
%e A367573    7,  24,  25;
%e A367573   11,  60,  61;
%e A367573   15, 112, 113;
%e A367573   23, 264, 265;
%e A367573   ...
%e A367573 Row n = (a, b, c) = (2*p + 1, 2*p^2 + 2*p, 2*p^2 + 2*p + 1), where p is the n-th prime number.
%e A367573 This sequence is the middle column.
%Y A367573 Cf. A072055 (short leg).
%K A367573 nonn,easy
%O A367573 1,1
%A A367573 _Miguel-Ángel Pérez García-Ortega_, Nov 23 2023