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A369497
Table read by rows: row n is the unique primitive Pythagorean triple (a,b,c) such that (a-b+c)/2 = prime(n+2) and whose short leg "a" is even.
1
8, 15, 17, 12, 35, 37, 20, 99, 101, 24, 143, 145, 32, 255, 257, 36, 323, 325, 44, 483, 485, 56, 783, 785, 60, 899, 901, 72, 1295, 1297, 80, 1599, 1601, 84, 1763, 1765, 92, 2115, 2117, 104, 2703, 2705, 116, 3363, 3365, 120, 3599, 3601, 132, 4355, 4357, 140, 4899, 4901, 144, 5183, 5185, 156, 6083, 6085
OFFSET
1,1
COMMENTS
See Exercise 3.5 of the reference.
REFERENCES
Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2024.
LINKS
Miguel-Ángel Pérez García-Ortega, Ejercicio 3.5.
FORMULA
Row n = (a, b, c) = (2*p - 2, p^2 - 2*p, p^2 - 2*p + 2), where p = prime(n+2) = A000040(n+2).
EXAMPLE
Table begins:
n=1: 8, 15, 17;
n=2: 12, 35, 37;
n=3: 20, 99, 101;
n=4: 24, 143, 145;
n=5: 32, 255, 257;
CROSSREFS
Cf. A037168 (short leg), A040976 (inradius).
Sequence in context: A300860 A352989 A367335 * A031103 A179107 A160524
KEYWORD
nonn,easy,tabf
STATUS
approved