A372220 - OEIS

%I #13 May 19 2024 11:54:07

%S 17,20,20,33,31,42,42,67,49,72,72,113,71,110,110,171,97,156,156,241,

%T 127,210,210,323,161,272,272,417,199,342,342,523,241,420,420,641,287,

%U 506,506,771,337,600,600,913,391,702,702,1067,449,812,812,1233,511,930,930,1411,577,1056,1056,1601

%N Four-column table read by rows: row n is the unique primitive Pythagorean quadruple (a,b,c,d) such that a > (a + b + c - d)/2 = 2n(n + 1) and b = c.

%C A Pythagorean quadruple is a quadruple (a,b,c,d) of positive integers such that a^2 + b^2 + c^2 = d^2 with a <= b <= c. Its inradius is (a+b+c-d)/2, which is a positive integer.

%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="/A372220/a372220.pdf">Teorema 10.13</a>

%F Row n = (a, b, c, d) = (2n^2 + 4n + 1, 4n^2 + 2n, 4n^2 + 2n, 6n^2 + 4n + 1).

%e Table begins:

%e   n=2:   17,   20,    20,    33;

%e   n=3:   31,   42,    42,    67;

%e   n=4:   49,   72,    72,   113;

%e   n=5:   71,  110,   110,   171;

%e   n=6:   97,  156,   156,   241;

%t cuaternas={};Do[cuaternas=Join[cuaternas,{2n^2+4n+1,4n^2+2n,4n^2+2n,6n^2+4n+1}],{n,2,35}];cuaternas

%Y Cf. A372219, A056220 (first column), A002943 (second column), A080859 (fourth column).

%K nonn,easy,tabf

%O 2,1

%A _Miguel-Ángel Pérez García-Ortega_, Apr 22 2024