# [seqfan] Re: Sequence Idea

Neil Sloane njasloane at gmail.com
Sat Oct 4 19:38:49 CEST 2014

```The quadratic residues mod 7 are 1,2,4, the nonresidues are 3,5,6.
Zero is a square mod 7, but isn't usually regarded as a quadratic residue.

There are several questions about A248222.
1. How is it defined?
2. Why is a(7) = 3 ?
3. We ought to have "maximal gap between squares mod n" too.
4. There is the question of "consecutive" versus "all" (gap between
consecutive QR's seems more natural) - in fact, what does "gap" mean?
5. If we write the numbers mod 7 in a circle, it is natural to include 0.
Then we could look at gaps (between QRs, or between squares)

If n is not a prime, there is an even bigger difference between "squares"
and "QRs". For m to be a QR, we must have gcd(m,n) = 1.

In short, there might be 4 or 8 versions of this sequence

On Sat, Oct 4, 2014 at 12:59 PM, M. F. Hasler <oeis at hasler.fr> wrote:

> David,
> I agree & propose it as https://oeis.org/draft/A248222.
> Best,
> Maximilian
>
>
> On Sat, Oct 4, 2014 at 9:03 AM, David Wilson <davidwwilson at comcast.net>
> wrote:
> > Maximum gap between quadratic residues mod n.
> >
> >
> >
> > Starting at n = 1, I believe a =
> (1,1,2,3,3,2,3,4,3,3,4,5,5,3,5,7,4,3,5,7,
> > ...)
> >
> >
> >
> > I don't think this is in the OEIS.
> >
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
>
>
>
> --
> Maximilian
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>

--
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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.