A372220 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.
17, 20, 20, 33, 31, 42, 42, 67, 49, 72, 72, 113, 71, 110, 110, 171, 97, 156, 156, 241, 127, 210, 210, 323, 161, 272, 272, 417, 199, 342, 342, 523, 241, 420, 420, 641, 287, 506, 506, 771, 337, 600, 600, 913, 391, 702, 702, 1067, 449, 812, 812, 1233, 511, 930, 930, 1411, 577, 1056, 1056, 1601
Offset: 2
Examples
Table begins: n=2: 17, 20, 20, 33; n=3: 31, 42, 42, 67; n=4: 49, 72, 72, 113; n=5: 71, 110, 110, 171; n=6: 97, 156, 156, 241;
References
- Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2024.
Links
- Miguel-Ángel Pérez García-Ortega, Teorema 10.13
Programs
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Mathematica
cuaternas={};Do[cuaternas=Join[cuaternas,{2n^2+4n+1,4n^2+2n,4n^2+2n,6n^2+4n+1}],{n,2,35}];cuaternas
Formula
Row n = (a, b, c, d) = (2n^2 + 4n + 1, 4n^2 + 2n, 4n^2 + 2n, 6n^2 + 4n + 1).
Comments