A367573 Long legs of the only primitive Pythagorean triple whose inradius is the n-th prime and whose short leg is an odd number.

12, 24, 60, 112, 264, 364, 612, 760, 1104, 1740, 1984, 2812, 3444, 3784, 4512, 5724, 7080, 7564, 9112, 10224, 10804, 12640, 13944, 16020, 19012, 20604, 21424, 23112, 23980, 25764, 32512, 34584, 37812, 38920, 44700, 45904, 49612, 53464, 56112, 60204, 64440

Offset: 1

Author

Miguel-Ángel Pérez García-Ortega, Nov 23 2023

Keywords

• nonn
• easy

Comments

See Ejercicio 2.7. of García-Ortega.

Examples

			Triangles begin
   5,  12,  13;
   7,  24,  25;
  11,  60,  61;
  15, 112, 113;
  23, 264, 265;
  ...
Row n = (a, b, c) = (2*p + 1, 2*p^2 + 2*p, 2*p^2 + 2*p + 1), where p is the n-th prime number.
This sequence is the middle column.
		

Links

• Miguel-Ángel Pérez García-Ortega, Capítulo 2. Inradio, El Libro de las Ternas Pitagóricas.

Crossrefs

Cf. A072055 (short leg).

Formula

a(n) = 2*p^2 + 2*p where p is prime(n).