666 and godly numbers

[franktaw at netscape.net]

Well, we can easily state that the asymptotic density is zero: the 
density
of the numbers avoiding any valid string in any given base is zero.

Intuitively, I think the number of such numbers is, in fact, finite.  
It seems
to me that for n sufficiently large, you can always find a base where 
the
representation of the number starts with the given string.

Franklin T. Adams-Watters

-----Original Message-----
From: Joshua Zucker <joshua.zucker at gmail.com>

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?)