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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).
1
3, 4, 5, 5, 12, 13, 7, 24, 25, 11, 60, 61, 13, 84, 85, 17, 144, 145, 19, 180, 181, 23, 264, 265, 29, 420, 421, 31, 480, 481, 37, 684, 685, 41, 840, 841, 43, 924, 925, 47, 1104, 1105, 53, 1404, 1405, 59, 1740, 1741, 61, 1860, 1861, 67, 2244
OFFSET
2,1
COMMENTS
See Corolario 5.2.3 of the reference.
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, Capítulo 5.
FORMULA
Row n = (a, b, c) = (p, ( p^2 - 1 ) / 2, ( p^2 + 1 ) / 2), where p = prime(n) = A000040(n).
EXAMPLE
Table begins:
n=2: 3, 4, 5;
n=3: 5, 12, 13;
n=4: 7, 24, 25;
n=5: 11, 60, 61;
n=6: 13, 84, 85;
...
MATHEMATICA
Apply[Join, Map[{#, (#^2-1)/2, (#^2+1)/2}&, Prime[Range[2, 31]]]]
CROSSREFS
Cf. A000040, A065091 (short leg), A216244 (long leg), A066885 (hypotenuse), A005097 (inradius).
Sequence in context: A370731 A151555 A263728 * A103606 A139794 A369493
KEYWORD
nonn,easy,tabf
STATUS
approved