[seqfan] Re: Another characterization of A244031?

[David Wilson]

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
> 
> --
> Seqfan Mailing list - http://list.seqfan.eu/