A245616 Pythagorean Threesomes: triples of natural numbers defining the six legs of three Pythagorean triangles.

44, 117, 240, 240, 252, 275, 88, 234, 480, 85, 132, 720, 160, 231, 792, 132, 351, 720, 480, 504, 550, 176, 468, 960, 170, 264, 1440, 220, 585, 1200, 720, 756, 825, 320, 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

Offset: 1

Author

Andreas Boe, Nov 05 2014

Keywords

• nonn

Comments

The sequence is sorted by increasing sums of triples and secondly by increasing order of first term.

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.

The sequence was calculated for the science fiction novel "The Fifth Jack" by Andreas Boe, Amazon books, 2014.

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

Examples

			(44,117,240)  sqrt(44^2+117^2)=125  sqrt(117^2+240^2)=267 sqrt(240^2+44^2)=244
		

Links

• Andreas Boe, Table of n, a(n) for n = 1..285

Crossrefs

Same numbers sorted gives A195816.

Cf. A268396.

Formula

x,y,sqrt(x^2+y^2) y,z,sqrt(y^2+z^2) z,x,sqrt(z^2+x^2)

Extensions

Edited by N. J. A. Sloane, Feb 11 2016