[seqfan] Re: Knights-move Ulam-Warburton - nice problem

Allan Wechsler acwacw at gmail.com
Wed Dec 19 03:30:07 CET 2018

I think few of us would disagree that the long-term answer is to replace
the current canned, precomputed graphs with an HTML5-based graphing tool,
which would allow the OEIS user to fiddle with scaling and transformation
of graphs completely on the browser side, placing no additional load on the
server, and allowing researchers to follow intuitions of the kind that led
me to ask for this particular graph to be rescaled.

I also understand that this would take a respectable development effort,
and I don't expect to see it soon.

Finally, I have to confess that the rescaling I asked for revealed exactly
nothing, completely violating my expectations. My intuition was completely
wrong in this case.

That just makes the mystery of this sequence deeper. It looks like chaos --
and then magically, at every 2^n+1 step, the stars align and the value
drops to 8. It's witchcraft. Can anyone prove any of Hasler's experimental

On Tue, Dec 18, 2018 at 2:26 AM Hugo Pfoertner <yae9911 at gmail.com> wrote:

> Allan,
> the question is more general. When is it justified to add a graph that is
> more or less duplicating the result of the internal graph function?
> https://oeis.org/A322049/graph
> The reason to add a scatterplot with logarithmic scale of the y-axis is to
> de-clutter the low value region of the graph.
> Adding a zoomable linear (pdf-)version is trivial, but I hesitate to open
> this can of worms.
> Hugo
> On Tue, Dec 18, 2018 at 4:08 AM Allan Wechsler <acwacw at gmail.com> wrote:
> > The graphs of the difference sequences (A319019, A322050) strongly
> suggest
> > some kind of self-similarity under the a map that takes 1+n to 1+2n. This
> > is a very vague hint as to a possible direction of work.
> >
> > Would it be possible to change the scatterplot from logarithmic to
> linear?
> > I have a feeling the logarithmic representation is hiding a lot of
> > possibly-suggestive structure near the upper rim of the graph. Also, I
> see
> > a lot of vaguely log-n-shaped curves, which would be straight lines in a
> > linear representation.
> >
> >
> --
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