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

[David Seal]

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
> >
> >
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> >
> 
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