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

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

Table of n, a(n) for n=2..54.

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

Adjacent sequences: A370757 A370758 A370759 * A370761 A370762 A370763

Keyword

nonn,easy,tabf

Author

Miguel-Ángel Pérez García-Ortega, Mar 01 2024

Status

approved