[seqfan] Re: OEIS contest.

[Brad Klee]

Hi All,

It seems like the goal Neil has stated for the contest is to increase
quality of recorded sequences rather than quantity. Quality could also
improve by adding more and new attributes to pre-existing sequences. It
could be time to review the list of "suggestions for new keywords" at:

https://oeis.org/wiki/Suggestions_for_new_keywords#Suggestions_for_new_keywords

But there really are unlimited opportunities to improve quality of the
encyclopedia through sequence _analysis_. Here is one example I found today:

Attribute: Range Restriction

All sequences in the database are restricted to integer numbers, but some
sequences have further restriction on the range. Odd positive numbers,
binary sequences, even positive numbers... those are easy examples of
sequences where the range can be restricted to: 2 N + 1, { 0, 1 }, 2 N,
with N the natural numbers.

I was learning about theta series in connection with one of the least
interesting and most unphysical Quantum Mechanics problems ( particle in a
3D box ), and found a slightly more difficult proof of maximum set for the
range of the sequence

https://oeis.org/A005875

which also describes quantum degeneracies. The series obviously has
something to do with cubic symmetry. Actually it is easy to figure out.

Points on x y or z axis always have degeneracy 6 except at the origin,
which is non-degenerate. Points in XY, YZ, ZX plane and not on x, y, z axis
have degeneracy 12 or degeneracy 24. In the remainder of space the
degeneracy is either 8 or 24. An elegant proof would use cosets and some
group theory, but I think it will suffice just to look at a table of
octahedral polyhedra of just one vertex figure and note the number of
vertices:

http://en.wikipedia.org/wiki/Octahedral_symmetry#Solids_with_full_octahedral_symmetry


Though ironically that table is missing the octahedron with 6 vertices.
>From the symmetry analysis it can be concluded that the range of A005875
occurs in a set no larger than:

1 \union 6 N \union 8 N,

where N is the natural numbers including zero. Looking around at the
crossrefs, it seems like other series would also have restricted domain.


Thanks,

Brad





On Sun, Nov 30, 2014 at 9:51 AM, Neil Sloane <njasloane at gmail.com> wrote:

> Ed,
> Charles and i discussed this. we were thinking
> of having a different kind of contest this year.
>
> one idea was to have a prize for the best explanation (formula, g.f.,
> recurrence) or proof of a conjecture for
> an existing sequence
>
> we didn't get around to discussing details.
>
> but we might - for instance - have a list of
> sequences where any formula is lacking. Or where
> there is an unproved conjecture
>
> An example is A098550.
>
> If people on this list like the idea, plse send me a list of A-numbers.
>
> btw, we also need to choose the winner of the A250000 prize.  i have a list
> of candidates, which i send out soon for comments
>
>
>
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
>
> On Sat, Nov 29, 2014 at 11:37 PM, L. Edson Jeffery <lejeffery2 at gmail.com>
> wrote:
>
> > Are there plans for another OEIS sequence contest coinciding with the
> > AMS/MAA conference that is coming up soon? If so, could someone please
> give
> > instructions and details as soon as possible? Thank you.
> >
> > Ed Jeffery
> >
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