A111105 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.

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

Offset

1,1

Comments

Subset of A024409. If only primitive triples with gcd(x,y,z)=1 are admitted, the sequence reduces to A137559.

Links

Robin Visser, Table of n, a(n) for n = 1..10000

R. A. Beuregard and 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], 2001.

R. Hartshorne and Ronald van Luijk, Non-Euclidean Pythagorean triples, a problem of Euler and rational points on K3 surfaces, arXiv:math/0606700 [math.NT], 2006.

Example

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).

Crossrefs

Cf. A137559.

Sequence in context: A069330 A218156 A160206 * A137559 A306097 A185377

Adjacent sequences: A111102 A111103 A111104 * A111106 A111107 A111108

Keyword

nonn

Author

R. J. Mathar, Apr 20 2008

Status

approved