[seqfan] Re: Why does this sequence make a staircase pattern?

[Neil Sloane]

Hans,  I have not been following this thread.  Can you be in charge of
making sure the sequences - and your amazing graph - are in the OEIS,
please?

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 Sun, Feb 16, 2020 at 9:52 AM Hans Havermann <gladhobo at bell.net> wrote:

> EB: "How did you find it? And could you please compute some more terms?"
>
> I've shared my Mathematica code with Elijah. I'm currently approaching
> 10^9 in my record-length "order" search and a log graph nicely illustrates
> the "staircase":
>
> http://chesswanks.com/num/EB'sOrderStaircase.png
>
> "... why could these 'plateaus' and 'cliffs' occur?"
>
> Each number represents a record-length sequence so it shouldn't be too
> surprising that we might have to climb some distance to find a new one. The
> sequences themselves have the characteristic, often, of being extendable by
> prepending another number. Sometimes, when we are in new territory, this
> can be done many times. In the plateaus, we extend our records by
> exhausting this feature in the nearby integer terrain.
>
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