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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,tabf,more
AUTHOR
STATUS
approved

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Last modified April 14 09:38 EDT 2024. Contains 371657 sequences. (Running on oeis4.)