[seqfan] Re: Another characterization of A244031?

[Neil Sloane]

Concerning A244031, about which Maximilan said

`The current definition is indeed a bit "obfuscated" (i.e. useless
complicated), and I'd be in favour of the proposed rephrasing.`

let me say that I prefer the original definition, which is

Positive numbers n such that the quadratic form x^2+n*y^2 does not
represent a prime strictly between n and 2n.

and is based on the paper by my friends Bill Jagy and Kap Kaplansky.
I don't agree that it is "useless complicated".

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 Tue, May 8, 2018 at 9:52 AM, Marc LeBrun <mlb at well.com> wrote:

> If you haven't already, I suggest that if you change the definition you
> still retain a comment giving the alternate form (eg to help folks
> searching on "quadratic form").
>
> > On May 7, 2018, at 7:36 PM, David Wilson <davidwwilson at comcast.net>
> wrote:
> >
> > Aha.
> >
> > I generated the sequence independently using my simpler definition, and
> looking up the terms yielded A244031.
> > When I saw that A244031 was NJAS's sequence, I assumed the quadratic
> form characterization was a necessary part of the definition.
> > But as MFH show, the quadratic form characterization trivially devolves
> to my simpler characterization.
> >
> > I assume this is also the case for A244029 and A244030 as well (which
> appear to be the prime and composite elements, respectively, of A244031).
> >
> > Conjecturally, all these sequences are finite.
> >
> >> -----Original Message-----
> >> From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of M. F.
> >> Hasler
> >> Sent: Monday, May 07, 2018 12:32 PM
> >> To: Sequence Fanatics Discussion list
> >> Subject: [seqfan] Re: Another characterization of A244031?
> >>
> >> On Sat, May 5, 2018 at 8:47 AM, David Wilson wrote:
> >>
> >>> n such that 1 <= k^2 <= n   =>   n + k^2 is composite.
> >>>
> >>
> >> It's easy to see that this is completely equivalent, because y has to
> be equal
> >> to 1 in order to have
> >> x^2 + n y^2 strictly between n and 2n (and x^2 is never prime), so for
> the
> >> considered purpose,
> >> x^2 + n y^2 is equivalent to n + x^2.
> >>
> >> The current definition is indeed a bit "obfuscated" (i.e. useless
> complicated),
> >> and I'd be in favour of the proposed rephrasing.
> >>
> >> - Maximilian
> >>
> >> --
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> >
> >
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>
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