%I #14 Jan 03 2024 08:16:45
%S 697,925,1073,1105,1394,1850,2091,2146,2165,2210,2665,2775,2788,3219,
%T 3277,3315,3485,3700,3965,4181,4182,4225,4292,4330,4420,4453,4625,
%U 4879,5330,5365,5525,5550,5576,6005,6273,6438,6475,6495,6554,6630,6970,7085
%N 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.
%C Subset of A024409. If only primitive triples with gcd(x,y,z)=1 are admitted, the sequence reduces to A137559.
%H Robin Visser, <a href="/A111105/b111105.txt">Table of n, a(n) for n = 1..10000</a>
%H R. A. Beuregard and E. R. Suryanarayan, <a href="http://www.jstor.org/stable/2690724">Pythagorean Boxes</a>, Math. Mag. vol 74 no 3 (2001) pp 222-227.
%H J. Fricke, <a href="https://arxiv.org/abs/math/0112239">On Heron simplices and integer embedding</a>, arXiv:math/0112239 [math.NT], 2001.
%H R. Hartshorne and Ronald van Luijk, <a href="https://arxiv.org/abs/math/0606700">Non-Euclidean Pythagorean triples, a problem of Euler and rational points on K3 surfaces</a>, arXiv:math/0606700 [math.NT], 2006.
%e a(1)=697 represents the (z,y,x)-triples (697,185,153) and (697,680,672).
%e a(4)=1105 represents the triples (1105,520,264), (1105,561,264), (1105,1073,952) and (1105,1073,975).
%Y Cf. A137559.
%K nonn
%O 1,1
%A _R. J. Mathar_, Apr 20 2008
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