[seqfan] Re: Natural log e in the Pascal system

[Jess Tauber]

Nice site, Peter, but I don't know whether G+ would make me take Google
Chrome, which I hate.

In any case I wanted to see whether Harlan Brothers' procedure would give
interesting results on other straight-line relations in the Pascal system.
The only other finite sequences, over positive powers of ten, come from the
shallow diagonals.

If you take these terms instead of those from rows you get TWO alternating
patterns. In the first the resulting numbers keep getting smaller, while
those of the second keep getting larger, in a regular way determined by
multiplying previous results by sequences of fractions. I had hoped they
might end up as limits the way the row results do, and related to e, but
they don't.

And the results are set up in such a way that if the two sets are properly
aligned, products of pairs of terms, one from each set, are always exactly
2. Could this coordination imply a relationship to some constant of a
different identity?

Jess Tauber


On Thu, Sep 5, 2013 at 3:07 AM, Peter Luschny <peter.luschny at gmail.com>wrote:

> Yes. Our sister site on G+ reported this on May 05.
> https://plus.google.com/u/0/communities/113220522707815729771
>
> You are welcome to visit us (and perhaps contribute?) there.
> Peter
>
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