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

Author

Miguel-Ángel Pérez García-Ortega, Jan 24 2024

Keywords

• nonn
• easy
• tabf

Comments

See Exercise 3.5. of the reference.

Examples

			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;
		

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, Ejercicio 3.5.

Crossrefs

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

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).