[seqfan] Re: Integral sets of points (A007285, A096872 and A096873)

[Benoît Jubin]

On Wed, Nov 16, 2011 at 9:21 PM,  <israel at math.ubc.ca> wrote:
> For A007285, you can't have 1 or 2 points "not all on a line", so I don't
> think there should be a(1) or a(2)..

You're very right: I first thought of adding a(1) and a(2), and then I
noticed that the definition should mention "not all on a line", and I
didn't reconsider the silliness of a(1) and a(2) in this new light!


>
> Robert Israel                            israel at math.ubc.ca
> Department of Mathematics    http://www.math.ubc.ca/~israel
> University of British Columbia        Vancouver, BC, Canada
>
> On Nov 16 2011, Benoît Jubin wrote:
>
>> Dear Seqfans,
>>
>> 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.
>> modify: a(1)=0
>>
>> A096873: Minimum diameter of an integral set of n points in the plane,
>> no 3 on a line, no 4 on a circle.
>> modify: a(1)=0
>> 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?
>>
>> Thanks,
>> Benoit
>>
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