[seqfan] Re: Brief names for A234741 and A234742 wanted.

M. F. Hasler oeis at hasler.fr
Sun Feb 16 16:57:10 CET 2014


Dear Antti & SeqFans,

I suggest to go slowly with inventing new (potentially "obscure")
terminology,
at least it should IMHO not be used in the %NAME, but maybe rather
suggested in the comments.
I proposed to simplify %N A234742 to

Product of the binary encodings of the irreducible factors (with
multiplicity) of the GF(2)[X]-polynomial whose encoding is n.
and added the explaining comment

The product is the straightforward product of integers.

see https://oeis.org/draft/A234742
(These are just suggestions in reply to the request ; I don't want at all
to impose my personal ideas.)

Maximilian


On Sat, Feb 15, 2014 at 6:28 PM, Antti Karttunen
<antti.karttunen at gmail.com>wrote:

> On Sat, Feb 15, 2014 at 10:29 PM, Antti Karttunen
> <antti.karttunen at gmail.com> wrote:
> > Cheers,
> >
> > For several reasons I would like to have brief nicknames for these two
> > sequences:
> >
> > http://oeis.org/A234741 a(n) = Number obtained when the prime divisors
> > of n are multiplied together as (encodings of) GF(2)[X]-polynomials
> > (without carry-bits, as in A048720).
> > and:
> > http://oeis.org/A234742 a(n) = Number obtained when the binary
> > encodings of irreducible polynomial factors of GF(2)[X]-polynomial
> > whose encoding n is, are multiplied together normally, as natural
> > numbers, with carry-bits having their effect.
> >
> > I have been thinking about neologisms such as "downcarrying" for
> > A234741 and "upcarrying" for A234742. But maybe they should also
> > reflect that process akin of "unfolding open" and then "folding it
> > again", but by "different creases"?
> >
> > (You may think that these sequences are about
> > "unlawfully" mixing division & multiplication operations in two
> > different rings, Z and GF(2)[X] polynomials)
> >
> > Also wondering whether Marc LeBrun's "rebasing" terminology would fit
> > here somehow?
> > (E.g. A234741 = "Number rebased to GF(2)[X] by its prime divisors" ?
> No...)
> >
> > Any suggestions are welcome.
> >
>
> I think I found it:
>
> I will talk about "downward remultiplication (Z -> GF(2)[X])" and
> "upward remultiplication (GF(2)[X] -> Z)" of numbers.
> I realized also funny etymological truth: multiply = multi+ply, where
> ply ~ fold ~ bend. At least according to Wiktionary, which I admit,
> sometimes lies:
> http://en.wiktionary.org/wiki/multiply#Etymology_1
>
>
> Then the sorted version of A234742 (with duplicates removed)
> https://oeis.org/draft/A236842
> would have a name like:
> "Numbers which occur as results of upward remultiplication (GF(2)[X]
> -> Z, A234742) of some number."
>
> And a sequence like:
> https://oeis.org/draft/A236834
> would be:
> "Numbers which do not occur as a result of downward remultiplication
> (Z -> GF(2)[X], A234741) of any number."
>
>
> Any objections or better ideas?
>
>
>
> >
> >
> > Thanks,
> >
> > Antti
>
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>
> Seqfan Mailing list - http://list.seqfan.eu/
>



-- 
Maximilian


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