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.

3, 4, 5, 5, 12, 13, 9, 40, 41, 13, 84, 85, 21, 220, 221, 25, 312, 313, 33, 544, 545, 37, 684, 685, 45, 1012, 1013, 57, 1624, 1625, 61, 1860, 1861, 73, 2664, 2665, 81, 3280, 3281, 85, 3612, 3613, 93, 4324, 4325, 105, 5512, 5513, 117, 6844, 6845, 121, 7320, 7321, 133, 8844, 8845, 141, 9940, 9941

Offset

1,1

Comments

See Exercise 3.5. 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=1..60.

Miguel-Ángel Pérez García-Ortega, Ejercicio 3.5.

Formula

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).

Example

Table begins:
  n=1:   3,   4,   5;
  n=2:   5,  12,  13;
  n=3:   9,  40,  41;
  n=4:  13,  84,  85;
  n=5:  21, 220, 221;

Crossrefs

Cf. A000040, A076274 (short leg), A006093 (inradius).

Sequence in context: A370760 A103606 A139794 * A365796 A202819 A185383

Adjacent sequences: A369490 A369491 A369492 * A369494 A369495 A369496

Keyword

nonn,easy,tabf

Author

Miguel-Ángel Pérez García-Ortega, Jan 24 2024

Status

approved