666 and godly numbers

[Joshua Zucker]

On Tue, Mar 4, 2008 at 10:36 AM, Jonathan Post <jvospost3 at gmail.com> wrote:
> It is a Category Error, philosophically, to confuse a string of
>  numerals with something that they represent outside of the abstract
>  world of integer arithmetic (i.e. 666 = Satan, or 888 = Jesus).
>
>  Nonetheless, you can easily verify with Googling that "888" is the
>  genuinely "godly" number in Christian numerology, which derived from
>  Hebrew Gematria. I can visualize njas wincing when he sees this.
>  Sorry, Neil.

I would ordinarily apologize to Neil for such a silly sequence, but I
think that the concept (are there infinitely many godly numbers?)
generalizes nicely, and so 666 is just an example of a string of
base-b digits to avoid.  If there are infinitely many godly numbers
then presumably the same will be true for any string in base b.

Does anyone have an answer to that original question, of how many
numbers there are that avoid the digits 666 in every base?  (Is it
infinitely many, and if so what can we say about their asymptotic
density?)

--Joshua