[seqfan] Re: Extending signature sequences for transcendental numbers

[Kerry Mitchell]

On Mon, Jun 21, 2010 at 3:50 PM, Robert Israel <israel at math.ubc.ca> wrote:

> Unless I misunderstand you, if 0 < x < 1 every entry in T(x) will be 1.
> It makes no difference whether x is transcendental.  It's just that
> k x^n < 1 for all k < x^(-n), so at least the first floor(x^(-n)) entries
> of Sn(x) will be 1.
>
> Robert Israel                                israel at math.ubc.ca
> Department of Mathematics        http://www.math.ubc.ca/~israel<http://www.math.ubc.ca/%7Eisrael>
> University of British Columbia            Vancouver, BC, Canada
>
>
Yes, that's correct.  So, for 0 < x < 1, I looked at the sequences of the
a_n coefficients.  This is equivalent to looking at the a_0 coefficients for
1/x, as Franklin pointed out.

Kerry
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