A367573 Table read by rows: row n is the only primitive Pythagorean triple whose inradius is the n-th prime and whose short leg is an odd number.

5, 12, 13, 7, 24, 25, 11, 60, 61, 15, 112, 113, 23, 264, 265, 27, 364, 365, 35, 612, 613, 39, 760, 761, 47, 1104, 1105, 59, 1740, 1741, 63, 1984, 1985, 75, 2812, 2813, 83, 3444, 3445, 87, 3784, 3785, 95, 4512, 4513, 107, 5724, 5725

Offset

1,1

Comments

See Ejercicio 2.7. of the reference file.

References

J. M. Blanco Casado, J. M. Sánchez Muñoz, and M. A. Pérez García-Ortega, El Libro de las Ternas Pitagóricas, Preprint 2023.

Links

Table of n, a(n) for n=1..48.

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

Formula

Row n = (a, b, c) = (2p + 1, 2p^2 + 2p, 2p^2 + 2p + 1), where p is the n-th prime number.

Example

Triples begin
   5,  12,  13;
   7,  24,  25;
  11,  60,  61;
  15, 112, 113;
  23, 264, 265;
  ...

Mathematica

n=16; primos={}; Do[primos=Join[primos, {2 Prime[i]+1, 2Prime[i]^2+2Prime[i], 2Prime[i]^2+2Prime[i]+1}], {i, 1, n}]; primos

Crossrefs

Cf. A072055 (short leg).

Sequence in context: A259860 A268035 A223255 * A076537 A263580 A110134

Adjacent sequences: A367570 A367571 A367572 * A367574 A367575 A367576

Keyword

nonn,tabf,more

Author

Miguel-Ángel Pérez García-Ortega, Nov 23 2023

Status

approved