A367335 Table read by rows: row n is the only primitive Pythagorean triple whose inradius is the n-th odd prime and whose short leg is an even number.

8, 15, 17, 12, 35, 37, 16, 63, 65, 24, 143, 145, 28, 195, 197, 36, 323, 325, 40, 399, 401, 48, 575, 577, 60, 899, 901, 64, 1023, 1025, 76, 1443, 1445, 84, 1763, 1765, 88, 1935, 1937, 96, 2303, 2305, 108, 2915, 2917, 120, 3599, 3601, 124, 3843, 3845, 136, 4623, 4625

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..54.

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

Formula

Row n = (a, b, c) = (2*p + 2, p^2 + 2*p, p^2 + 2*p + 2), where odd prime p = prime(n+1) = A065091(n).

Example

Triples begin
    8,  15,  17;
   12,  35,  37;
   16,  63,  65;
   24, 143, 145;
   28, 195, 197;
   ...

Mathematica

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

Crossrefs

Cf. A065091, A089241 (short leg).

Sequence in context: A114605 A300860 A352989 * A369497 A031103 A179107

Adjacent sequences: A367332 A367333 A367334 * A367336 A367337 A367338

Keyword

nonn,easy,tabf

Author

Miguel-Ángel Pérez García-Ortega, Nov 23 2023

Status

approved