A111105 Largest member z of a triple 0

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

Author

R. J. Mathar, Apr 20 2008

Keywords

• nonn

Comments

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

Examples

			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).
		

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.

Crossrefs

Cf. A137559.