[seqfan] Re: followup Re: Floretions CKD

[P. Michael Hutchins]

Re "Neither CKD nor anyone else seems to have performed the automated
search to re-discover how to calculate the mystery sequences.":

It almost sounds like you (Robert) did.

In any case, wouldn't it be nice if someone (having done so) were to
"publish"(*) that info on OEIS?!
(*: assuming that OEIS now has some way of such being made sufficiently
easily available as to make that truly worthwhile (as opposed to only being
able to "publish" such as part of a Sequence Entry)
(Perhaps there is now a way, somehow via the Wiki.)
)
(*: assuming that O

On Sun, Apr 28, 2024 at 6:42 AM Robert Munafo <mrob27 at gmail.com> wrote:

> Thank you Bob and Kevin and Richard.
>
> Bob Lyons wrote:
> > I'm not familiar with floretions.
> > But back in March, Neil and I discussed the FAMP programs and the fact
> that there doesn't seem to be an easy way to run these programs.
> > Neil asked me to move all the FAMP programs from the PROG section to the
> COMMENTS section.
>
> Thank you. Later (after my previous message to seqfan) Creighton
> Dement (CKD) wrote back to me, stating that some of the early OEIS
> sequences were "not meant to be published" even though they were on a
> website. My notes from 15 years ago indicate that at the time, he had
> told me that the sequences came from a website whose contents were
> lost somehow (and had no backups). Neither CKD nor anyone else seems
> to have performed the automated search to re-discover how to calculate
> the mystery sequences. I guess if they're still in the OEIS after all
> these years then they can stay.
>
> Kevin Ryde wrote:
> > > integers taken 3 bits at a time
> > That's A308496 (mentioned in the PDF). The material there is still
> controversial.
> >
> > > quasi ring-like algebraic system with 16 basis elements (but not
> normal sedenions).
> > That might be "order 2".
> > I thought the intention was what might be called a direct product of
> some number of quaternions.  The algebraists in the house will probably say
> that's badly wrong terminology. (Is "Clifford algebra" closer?)
>
> Okay, that seems to explain what CKD meant, saying that "order 2" was
> the result of doing some kind of construction once (and that each
> subsequent application of the construction multiplies the number of
> basis elements by 4). I personally think CKD has recently invented an
> iterable construction, vaguely like Cayley-Dickson in principle, that
> repeats a pattern that he recognised in his earlier work; and I think
> he now considers the earlier work to (retroactively) be part of the
> series.
>
> Richard Mathar wrote:
> > Back in 2010 Floretions were an algebra defined on a group of order 32.
> I tried to put the group into a standard perspective then:
> https://oeis.org/A173343/a173343.pdf .
>
> Thanks for reminding me, yes I do have that paper and I've just linked
> to it from my old Floretions-related web page.
> (mrob.com/pub/seq/floretion.html)
>
> I see that it hasn't gotten any more well-understood, and the new
> stuff is too confusing for me: using 64 or 256 or more real numbers at
> a time, somehow using integers as indices to the basis vectors, and
> using the same noun "floretions" to refer to the integer and to a
> compound of many reals.
>
> --
>   Robert Munafo, mrob27 at gmail.com
>
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> Seqfan Mailing list - http://list.seqfan.eu/
>