# [seqfan] Re: Another characterization of A244031?

Marc LeBrun mlb at well.com
Tue May 8 15:52:08 CEST 2018

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

```