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A369493 Table read by rows: row n is the unique primitive Pythagorean triple (a,b,c) such that (a-b+c)/2 = prime(n) and the short leg "a" is odd.

%I A369493 #21 Feb 26 2024 10:38:02
%S A369493 3,4,5,5,12,13,9,40,41,13,84,85,21,220,221,25,312,313,33,544,545,37,
%T A369493 684,685,45,1012,1013,57,1624,1625,61,1860,1861,73,2664,2665,81,3280,
%U A369493 3281,85,3612,3613,93,4324,4325,105,5512,5513,117,6844,6845,121,7320,7321,133,8844,8845,141,9940,9941
%N A369493 Table read by rows: row n is the unique primitive Pythagorean triple (a,b,c) such that (a-b+c)/2 = prime(n) and the short leg "a" is odd.
%C A369493 See Exercise 3.5. of the reference.
%D A369493 Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2024.
%H A369493 Miguel-Ángel Pérez García-Ortega, <a href="/A369493/a369493.pdf">Ejercicio 3.5</a>.
%F A369493 Row n = (a, b, c) = (2*p - 1, 2*p^2 - 2*p, 2*p^2 - 2*p + 1), where p = prime(n) = A000040(n).
%e A369493 Table begins:
%e A369493   n=1:   3,   4,   5;
%e A369493   n=2:   5,  12,  13;
%e A369493   n=3:   9,  40,  41;
%e A369493   n=4:  13,  84,  85;
%e A369493   n=5:  21, 220, 221;
%Y A369493 Cf. A000040, A076274 (short leg), A006093 (inradius).
%K A369493 nonn,easy,tabf
%O A369493 1,1
%A A369493 _Miguel-Ángel Pérez García-Ortega_, Jan 24 2024