%I #20 Mar 25 2024 21:50:37
%S 3,4,5,5,12,13,7,24,25,11,60,61,13,84,85,17,144,145,19,180,181,23,264,
%T 265,29,420,421,31,480,481,37,684,685,41,840,841,43,924,925,47,1104,
%U 1105,53,1404,1405,59,1740,1741,61,1860,1861,67,2244
%N Table read by rows: row n is the unique primitive Pythagorean triple (a,b,c) such that a = prime(n).
%C See Corolario 5.2.3 of the reference.
%D Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2024.
%H Miguel-Ángel Pérez García-Ortega, <a href="/A370760/a370760.pdf">Capítulo 5</a>.
%F Row n = (a, b, c) = (p, ( p^2 - 1 ) / 2, ( p^2 + 1 ) / 2), where p = prime(n) = A000040(n).
%e Table begins:
%e n=2: 3, 4, 5;
%e n=3: 5, 12, 13;
%e n=4: 7, 24, 25;
%e n=5: 11, 60, 61;
%e n=6: 13, 84, 85;
%e ...
%t Apply[Join, Map[{#,(#^2-1)/2,(#^2+1)/2}&,Prime[Range[2,31]]]]
%Y Cf. A000040, A065091 (short leg), A216244 (long leg), A066885 (hypotenuse), A005097 (inradius).
%K nonn,easy,tabf
%O 2,1
%A _Miguel-Ángel Pérez García-Ortega_, Mar 01 2024