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A367335
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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.
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1
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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
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OFFSET
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1,1
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COMMENTS
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See Ejercicio 2.7. of the reference file.
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REFERENCES
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J. M. Blanco Casado, J. M. Sánchez Muñoz, and M. A. Pérez García-Ortega, El Libro de las Ternas Pitagóricas, Preprint 2023.
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LINKS
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FORMULA
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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).
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EXAMPLE
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Triples begin
8, 15, 17;
12, 35, 37;
16, 63, 65;
24, 143, 145;
28, 195, 197;
...
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MATHEMATICA
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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
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CROSSREFS
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KEYWORD
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nonn,easy,tabf
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AUTHOR
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STATUS
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approved
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