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A367573 Table read by rows: row n is the only primitive Pythagorean triple whose inradius is the n-th prime and whose short leg is an odd number. 1

%I #13 Dec 31 2023 00:52:40

%S 5,12,13,7,24,25,11,60,61,15,112,113,23,264,265,27,364,365,35,612,613,

%T 39,760,761,47,1104,1105,59,1740,1741,63,1984,1985,75,2812,2813,83,

%U 3444,3445,87,3784,3785,95,4512,4513,107,5724,5725

%N Table read by rows: row n is the only primitive Pythagorean triple whose inradius is the n-th prime and whose short leg is an odd number.

%C See Ejercicio 2.7. of the reference file.

%D J. M. Blanco Casado, J. M. Sánchez Muñoz, and M. A. Pérez García-Ortega, El Libro de las Ternas Pitagóricas, Preprint 2023.

%H Miguel-Ángel Pérez García-Ortega, <a href="/A367573/a367573.pdf">Capítulo 2. Inradio, El Libro de las Ternas Pitagóricas</a>.

%F Row n = (a, b, c) = (2p + 1, 2p^2 + 2p, 2p^2 + 2p + 1), where p is the n-th prime number.

%e Triples begin

%e 5, 12, 13;

%e 7, 24, 25;

%e 11, 60, 61;

%e 15, 112, 113;

%e 23, 264, 265;

%e ...

%t n=16;primos={};Do[primos=Join[primos,{2 Prime[i]+1,2Prime[i]^2+2Prime[i],2Prime[i]^2+2Prime[i]+1}],{i,1,n}];primos

%Y Cf. A072055 (short leg).

%K nonn,tabf,more

%O 1,1

%A _Miguel-Ángel Pérez García-Ortega_, Nov 23 2023

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Last modified May 20 12:27 EDT 2024. Contains 372712 sequences. (Running on oeis4.)