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

Antti Karttunen antti.karttunen at gmail.com
Sat Feb 15 23:28:17 CET 2014

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:

Then the sorted version of A234742 (with duplicates removed)
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:
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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