3 potentially new sequences

[Richard Mathar]

so one can create b-files with UNIX commands:
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Date: Tue, 11 Mar 2008 01:24:20 -0700
From: "Max Alekseyev" <maxale at gmail.com>
To: "Joshua Zucker" <joshua.zucker at gmail.com>
Subject: Re: 666 and godly numbers
Cc: "Jonathan Post" <jvospost3 at gmail.com>,
   "Maximilian Hasler" <maximilian.hasler at gmail.com>,
   "Sequence Fans" <seqfan at ext.jussieu.fr>
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On Tue, Mar 4, 2008 at 3:17 PM, Joshua Zucker <joshua.zucker at gmail.com> wrote:

>  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?)

Under some plausible probabilistic assumptions Rustem Aidagulov
proposed that the number of godly numbers is infinite if c < 1 and
futhermore, the number M(N) of godly numbers below N satisfies the
following asymptotic formula:

log( M(N) ) / log( N ) = (1 - c) * (1 + o(1))

where c = - sum[m=7..oo] log(1-1/m^3) / log(m).

Regards,
Max