[seqfan] Re: Numbers of the form n*(n+k)

[Brad Klee]

My thoughts exactly, plus I would say that A002378
(also twice triangular numbers), is a funny case study
of what not  to do. Compare definitions to comments
therein.

In standard zoology, a new taxonomic name is given
only upon discovery of a new taxon. When synonyms
occur, precedence is given by history.

In analogy, mathematical researchers should only
hope to put a name on something when they have
done relevant analysis or proving, originally if possible.

In contrast, I thought the terms "trithagorean" and
"pentathagorean" from recent development (Cf. [1,2])
were okay. Possibly not.

They meet David Seal's criterion of generalizing on
pre-existing nomenclature, and they also meet my
work-done criterion: the names signify that a proof
exists showing some particular property (in this case
that integer triples can correspond to lengths of sides
of triangles). To me, these terms also have a sense of
playfulness and humor, which I find refreshing.

It has now been a few weeks with no serious
counterargument. Either the proof is wrong or a
historical precedent has been ignored? (Hopefully
it's not personal prejudice, or disciplinary hatred.)
More likely it is just an issue of busy schedules,
and other vital issues.

We'll see what happens, maybe approval.

Cheers,

Brad

[1] https://oeis.org/draft/A309507
[2] https://oeis.org/draft/A330657

On Thu, Mar 19, 2020 at 12:15 PM David Seal <david.j.seal at gwynmop.com> wrote:
>
> I agree with Neil - though since I'm fairly certain I've never come across "oblong number" before in the ~55 years since I first encountered "square number" and "triangular number", I think there's a good case to be made that the old law has been broken in the past!
>
> And I would add another law that "if new terminology is needed, thou shalt modify related existing terminology in preference to inventing entirely new terminology". For instance, various modifications of the idea of "perfect number" have been created, and their names are modifications of the term, such as "k-perfect number", "k-imperfect number", "semiperfect number", "hemiperfect number", "hyperperfect number", "superperfect number", etc.
>
> So if you really do feel that you need terminology for this concept, I'd suggest basing it on the existing "oblong number", e.g. by using "k-oblong number" for numbers of the form n(n+k), rather than on an essentially new term such as "product number".
>
> David
>
>
> > On 19 March 2020 at 14:39 Neil Sloane <njasloane at gmail.com> wrote:
> >
> >
> > Don't think that is a good idea.  There is an old law that "thou shalt not
> > create new terminology unnecessarily".
> >
> > Let's stick to n(n+2).
> >
> > Best regards
> > Neil
> >
> > Neil J. A. Sloane, President, OEIS Foundation.
> > 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> > Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> > Phone: 732 828 6098; home page: http://NeilSloane.com
> > Email: njasloane at gmail.com
> >
> >
> >
> > On Thu, Mar 19, 2020 at 10:33 AM MARION <charliemath at optonline.net> wrote:
> >
> > > Dear SeqFans,
> > >
> > > I have a question regarding terminology.
> > >
> > > We call the terms of A000290   0, 1, 4, 9, ...  the (perfect) squares.
> > >
> > > We call the terms of A002378   0, 2, 6, 12 ... the oblongs.
> > >
> > > What do we call the terms of A005563  0, 3, 8, 15?
> > >
> > > What do we call the terms of A028552  0, 4, 10, 18?
> > >
> > > What do you think about calling them the +2products and +3products,
> > > respectively?  Thus, the squares would be the +0products and the oblongs,
> > > the +1products.  Note that I'm not advocating changing the way we refer to
> > > the squares or the oblongs.  I'm simply looking for another way to refer to
> > > the terms in sequences like A005563 and A028552.
> > >
> > > I would like to call them something other than "the numbers of the form
> > > n*(n+2)" or "the numbers of the form n*(n+3)."  Perhaps I'm just not aware
> > > of some other "shortcut."
> > >
> > > Thanks for any feedback,
> > >
> > > Charlie Marion
> > >
> > > Yorktown Heights New York
> > >
> > >
> > > --
> > > Seqfan Mailing list - http://list.seqfan.eu/
> > >
> >
> > --
> > Seqfan Mailing list - http://list.seqfan.eu/
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/