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A370760 Table read by rows: row n is the unique primitive Pythagorean triple (a,b,c) such that a = prime(n).

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