Re: Rote Ariffmetic

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RA.  Note 4

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Subj:  Universal Sequence Index (USI)?
Date:  Sat, 30 Jun 2001 12:34:01 -0400
From:  Jon Awbrey <jawbrey<at>oakland.edu>
  To:  Marc LeBrun <mlb<at>well.com>
  CC:  Sequence Fanatics <seqfan<at>@ext.jussieu.fr>

SeqFans,

Several recent notes have given me flashbacks to this old theme,
which I just realized how to express in more contemporary terms.
For some reason Marc's note makes me think of Conway's Fractran.

EIS is a resource that I will call "Lot_X", or "L_X" for short,
X being an index value to be named later.  I am tempted to let
X equal something between 1 and 7^2, but I do not know yet how
much of an initial segment might be needed for other resources.

I do not have a complete idea here, but here are a couple
of fragmentary ideas that may form the ingredients of one:

Ingredient 1.

If L_X^(L_A061396) = L_X^(L_A061396^1) is my initial sequence,
then the expression "L_X^(L_A061396^n)" might serve to denote
A061396's n-th element, although I don't want to fix this too
rigidly right yet as other ways of doing this may work better.

Ingredient 2.

Now, riffs are constituted in such a way as to yield a code value v(f)
for each finite partial function f : M -> M, where M = 1, 2, 3, 4, ...
Is there a good way of using this natural scheme to specify a sequence
in terms of references to other sequences, assuming that we can design
all the details of de/referencing to work out as elegantly as possible?
Exercise for the reader.  I'll think about it a bit and get back to you.

Jon Awbrey

Marc LeBrun wrote:
>
[Deleted because sent to a non-public list]

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