[seqfan] Integral sets of points (A007285, A096872 and A096873)
benoit.jubin at gmail.com
Thu Nov 17 03:07:36 CET 2011
I think a few initial values should be added/corrected in the
sequences A007285, A096872 and A096873, and that the definitions could
be modified to treat them in a uniform way. I propose the following;
can you confirm this is correct?
A007285: Minimum diameter of an integral set of n points in the plane,
not all on a line.
add: a(1)=0 and a(2)=1 (therefore modify offset to 1)
A096872: Minimum diameter of an integral set of n points in the plane,
no 3 on a line.
A096873: Minimum diameter of an integral set of n points in the plane,
no 3 on a line, no 4 on a circle.
add comment: As of 2011, it is not known if this sequence is finite.
For all three sequences:
add the definition: "An integral set is a set where all distances
between points are integers."
add the link: http://ginger.indstate.edu/ge/COMBIN/GEOMETRY/intdistance.html
Add three analog sequences where all points are furthermore required
to have integral coordinates?
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