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Search: id:A111105
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| A111105 |
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Largest member z of a triple 0<x<y<z such that z^2-y^2, z^2-x^2 and y^2-x^2 are perfect squares. |
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+0
2
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| 697, 925, 1073, 1105, 1394, 1850, 2091, 2146, 2165, 2210, 2665, 2775, 2788, 3219, 3277, 3315, 3485, 3700, 3965, 4181, 4182, 4225, 4292, 4330, 4420, 4453, 4625, 4879, 5330, 5365, 5525, 5550, 5576, 6005, 6273, 6438, 6475, 6495, 6554, 6630, 6970, 7085
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Subset of A024409. If only primitive triples with gcd(x,y,z)=1 are admitted, the sequence reduces to A137559.
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LINKS
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R. A. Beuregard, E. R. Suryanarayan, Pythagorean Boxes, Math. Mag. vol 74 no 3 (2001) pp 222-227.
J. Fricke, On Heron simplices and integer embedding, arXiv:math/0112239 [math.NT].
R. Hartshorne, Ronald van Luijk, Non-Euclidean Pythagorean triples, a problem of Euler, and rational points on K3 surfaces, arXiv:math/0606700 [math.NT]
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EXAMPLE
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a(1)=697 represents the (z,y,x)-triples (697,185,153) and (697,680,672).
a(4)=1105 represents the triples (1105,520,264), (1105,561,264), (1105,1073,952) and (1105,1073,975).
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CROSSREFS
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Cf. A137559.
Sequence in context: A048925 A048426 A069330 this_sequence A137559 A118059 A028500
Adjacent sequences: A111102 A111103 A111104 this_sequence A111106 A111107 A111108
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KEYWORD
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nonn
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AUTHOR
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R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 20 2008
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