# Request for information about basis representation

Jon Awbrey jawbrey at att.net
Fri Mar 4 04:24:08 CET 2005

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david,

here we are just talking about taking a basis representation in powers of b,
and substituting a complex number, say i, for b, then plotting the sequence
on the complex plane.  it's not really a basis rep in the target domain.

ja

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David C Terr wrote:
>
> How do you define a complex base?
>
> Dave
>
>   Jon Awbrey <jawbrey at att.net>
>   To:        SeqFan <seqfan at ext.jussieu.fr>
>   03/03/2005 11:30 AM
>   Subject:        Re: Request for information about basis representation
>
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>
> much fun can be had by varying the base over the complex plane ---
> e.g.,  replacing base 2 with base i yields pretty fractal pics
> as you run through the binary reps of the integers ...
>
> ja
>
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>
> Ralf Stephan wrote:
> >
> > > I'm interested in the algebraic properties of the set of numbers
> > > whose coefficients S are fixed but whose base varies from two to
> > > infinity.  In the case of 35, this set is {35, 247, 1029...}, or:
> >
> > The sequences 'replace 2^k with a^k in binary expansion of n'
> > are the square array of which your sequences form the columns.
> > The rows were treated in
> >
> > http://www.ark.in-berlin.de/dcgfproof.ps
> >
> > Hope this helps a bit,
> > ralf

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inquiry e-lab: http://stderr.org/pipermail/inquiry/
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