integer quadruples with all pairwise distances being squares

[Rainer Rosenthal]

Richard Mathar wrote:

>  Subject: NEW SEQUENCE FROM R. J. Mathar
> %I A000001
> %S A000001 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 7400 7511 7585 7667
> 7735 7930 7995 8325 8362 8364 8450 8584 8660 8840 8906 9061 9250 9657 9673
> 9758 9773 9831 9945 9997 10175 10455 10660 10730 10825 11050 11100 11152 11285
> 11713 11803 11849 11895 12010 12025 12155 12325 12543 12546 12675
> %N A000001 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 A000001 Subset of A024409. If only primitive triples with gcd(x,y,z)=1 are admitted, the
> sequences reduces to 697 925 1073 1105 2165 2665 3277 3485 3965 4181 4225 4453
> 5525 6005 7085 7585 9061 9673 9773 9997 11285 11713 11849 12325 ...
> %H A000001 R. Hartshorne, Ronald van Luijk, <a href="http://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]
> %H A000001 J. Fricke, <a href="http://arxiv.org/abs/math/0112239">On Heron simplices and integer embedding</a>, arXiv:math/0112239 [math.NT].
> %H A000001 R. A. Beuregard, E. R. Suryanarayan, <a href="http://www.jstor.org/stable/2690724">Pythagorean Boxes</a>, Math. Mag. vol 74 no 3 (2001) pp 222-227.
> %e A000001 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).
> %O A000001 1
> %K A000001 ,nonn,
> %A A000001 R. J. Mathar (mathar at strw.leidenuniv.nl), Apr 20 2008
> 

I have two questions regarding the reference to J. Fricke:

1. The archiv.org is asking for endorsers. It sounds to me as if submitters
   with endorsers are more welcome there. As I happen to know Jan Fricke
   from his various interesting postings in de.sci.mathematik and
   de.rec.denksport I would be glad if somebody would "endorse", whatever
   that means.

2. (This is really related to the OEIS):
   Having looked up "J. Fricke" in the OEIS I came across
   http://www.research.att.com/~njas/sequences/A119485  as well as
   http://www.research.att.com/~njas/sequences/A119486 and wondered
   about the "sequences in context" which seemed quite unrelated to
   me (kind of random, indeed). Am I mistaken?
   Example: what's got http://www.research.att.com/~njas/sequences/A002808
   to do with A119485?

Cheers,
Rainer Rosenthal
r.rosenthal at web.de