A369497 Table read by rows: row n is the unique primitive Pythagorean triple (a,b,c) such that (a-b+c)/2 = prime(n+2) and whose short leg "a" is even.

8, 15, 17, 12, 35, 37, 20, 99, 101, 24, 143, 145, 32, 255, 257, 36, 323, 325, 44, 483, 485, 56, 783, 785, 60, 899, 901, 72, 1295, 1297, 80, 1599, 1601, 84, 1763, 1765, 92, 2115, 2117, 104, 2703, 2705, 116, 3363, 3365, 120, 3599, 3601, 132, 4355, 4357, 140, 4899, 4901, 144, 5183, 5185, 156, 6083, 6085

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 - 2, p^2 - 2*p, p^2 - 2*p + 2), where p = prime(n+2) = A000040(n+2).

Example

Table begins:
  n=1:   8,  15,  17;
  n=2:  12,  35,  37;
  n=3:  20,  99, 101;
  n=4:  24, 143, 145;
  n=5:  32, 255, 257;

Crossrefs

Cf. A037168 (short leg), A040976 (inradius).

Sequence in context: A300860 A352989 A367335 * A031103 A179107 A160524

Adjacent sequences: A369494 A369495 A369496 * A369498 A369499 A369500

Keyword

nonn,easy,tabf

Author

Miguel-Ángel Pérez García-Ortega, Jan 24 2024

Status

approved