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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.
1
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.
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
KEYWORD
nonn,easy,tabf
STATUS
approved