# [seqfan] Re: Base-related sequences, please go factorial!

victor miller victorsmiller at gmail.com
Sat Oct 17 21:42:52 CEST 2009

```Your mention of factorial base (and the notation for the digits) made
me think of Hendrik Lenstra's entertaining paper "Profinite Fibonacci
Numbers" http://math.berkeley.edu/~hwl/papers/fibo.pdf which, among
other things shows that there's a unique continuous extension (which
is analytic) for the Fibonacci numbers to profinite numbers (which are
essentially infinitely long numbers in the factorial base), and there
are precisely 11 fixed points of the Fibonacci function.

Victor

On Fri, Oct 16, 2009 at 7:48 AM, Antti Karttunen
<antti.karttunen at gmail.com> wrote:
> And it would be very good if somebody computed in the factorial base
> ( http://www.research.att.com/~njas/sequences/A007623 )
> some of the most interesting base-10 sequences,
> or the nearest analogues.
>
> Usually this would produce two distinct sequences:
> one using factorial base notation (so one has to devise some ugly
> kludge when there appears  digits > 9. This one just for "human
> consumption"),
> and then the other version where the former sequence
> is interpreted in the factorial base and then rewritten in the normal
> decimal notation (thus avoiding the previous problem).
> It is these latter sequences that might have some interesting tangents
> outside of pure base-based doodling.
>
> (Cf. http://www.research.att.com/~njas/sequences/A126301
> vs. http://www.research.att.com/~njas/sequences/A126300
> for the difference.)
>
> Yours,
>
> Antti
>
>
> On Fri, Oct 16, 2009 at 9:13 AM, <seqfan-request at list.seqfan.eu> wrote:
>
>>
>> Message: 4
>> Date: Thu, 15 Oct 2009 07:59:55 -0700
>> From: Jonathan Post <jvospost3 at gmail.com>
>> Subject: [seqfan] Re: re Integers formed by concatenating primes
>> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>> Message-ID:
>>        <5542af940910150759u397a2f88u6c2eb939b7ed3acb at mail.gmail.com>
>> Content-Type: text/plain; charset=ISO-8859-1
>>
>> Rather than 1-at-a-time debasification (acid that neutralizes bases?),
>> I usually suggest giving the main diagonal of the array, and showing
>> the array, of such a seq parameterized by base k, with row 2 being the
>> binary seq, row 10 being the decimal seq, and so forth.
>>
>> On Thu, Oct 15, 2009 at 7:39 AM, Leroy Quet <q1qq2qqq3qqqq at yahoo.com>
>> wrote:
>> > Is the base 2 version in the EIS? I have not checked. What about this
>> sequence with other bases (3,4,5,6, etc)?
>> >
>> > In general, I suggest, someone should add all the base-2 missing 'base'
>> sequences that already exist in the database as base 10 versions (submitted
>> by Eric Angelini and others), and submit base 10 versions of 'base'
>> sequences that involve base 2 (submitted by me and others).
>> > And of course, someone could calculate and submit the base 3, base 4,
>> base 5, etc versions of both the base 10 and the base 2 sequences, if these
>> sequences do not already exist in the database.
>> > :)
>> >
>> > Thanks,
>> > Leroy Quet
>> >
>> >
>> > [ ( [ ([( [ ( ([[o0Oo0Ooo0Oo(0)oO0ooO0oO0o]]) ) ] )]) ] ) ]
>> >
>
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>

```

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