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

Benoît Jubin benoit.jubin at gmail.com
Thu Nov 17 21:07:35 CET 2011

I think we should keep A096872(1)=A096873(1)=0 and
A096872(2)=A096873(2)=1, because this is true with no need of a
special definition, and the sequence would then appear when searching

It would be great if you can add the three other sequences. Also, your
papers on integral sets in Z_n and on finite fields can produce some
interesting sequences and tables.

On Wed, Nov 16, 2011 at 10:26 PM, Sascha Kurz
<sascha.kurz at uni-bayreuth.de> wrote:
> I agree with Robert. To keep it consistent it would not add a(1), a(2) to
> A096872 and A096873 either.
> It would be indeed more precise to state that not all points are on a line
> and to explain the term "integral set".
> Even the existence of A096873(8) is an open problem.
> If the suggested three additional sequences are considered to be
> interesting I may compute or look up the values and submit them.
> BTW: Some literature may be added, e.g.
> A007285,A096872:
> * S. Kurz and A. Wassermann: On the minimum diameter of plane integral
> point sets, Ars Combinatoria, Vol. 101 (2011), Pages 265-287
> A096873:
> * T. Kreisel and S. Kurz: There are integral heptagons, no three points on
> a line, no four on a circle, Discrete and Computational Geometry Vol. 39
> Issue 4 (2008), Pages 786-790
> * J. Solymosi and F. de Zeeuw: On a Question of Erdős and Ulam,
> Discrete and Computational Geometry Vol. 43 Issue 2 (2010), Pages 393-401
> Best wishes,
> Sascha
> Am Do, 17.11.2011, 06:21, schrieb israel at math.ubc.ca:
>> 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)..
>> 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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