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%I #42 Feb 11 2016 12:29:28
%S 44,117,240,240,252,275,88,234,480,85,132,720,160,231,792,132,351,720,
%T 480,504,550,176,468,960,170,264,1440,220,585,1200,720,756,825,320,
%U 462,1584,264,702,1440,308,819,1680,255,396,2160,960,1008,1100,352,936,1920,480,693,2376,396,1053,2160,429,880,2340,340,528,2880
%N Pythagorean Threesomes: triples of natural numbers defining the six legs of three Pythagorean triangles.
%C The sequence is sorted by increasing sums of triples and secondly by increasing order of first term.
%C The three numbers in a Pythagorean Threesome define the lengths of three sides of a tetrahedron with all integer length edges and one right angle vertex.
%C The sequence was calculated for the science fiction novel "The Fifth Jack" by Andreas Boe, Amazon books, 2014.
%C I do not have that book, but this sequence is closely related to (and may be an erroneous version of) A268396. - _Arkadiusz Wesolowski_, Feb 03 2016
%H Andreas Boe, <a href="/A245616/b245616.txt">Table of n, a(n) for n = 1..285</a>
%F x,y,sqrt(x^2+y^2) y,z,sqrt(y^2+z^2) z,x,sqrt(z^2+x^2)
%e (44,117,240) sqrt(44^2+117^2)=125 sqrt(117^2+240^2)=267 sqrt(240^2+44^2)=244
%Y Same numbers sorted gives A195816.
%Y Cf. A268396.
%K nonn
%O 1,1
%A _Andreas Boe_, Nov 05 2014
%E Edited by _N. J. A. Sloane_, Feb 11 2016
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