# [seqfan] Re: defn of A167415

Neil Sloane njasloane at gmail.com
Sat Jun 15 10:16:06 CEST 2019

```Perhaps RJM could replace the existing definition of A167415 with Don
Reble's.

IIRC, Don isn't registered as an OEIS user (which is something I regret).

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 Fri, Jun 14, 2019 at 9:13 PM Don Reble via SeqFan <seqfan at list.seqfan.eu>
wrote:

>
> > How is A167415 defined?
>
>     It looks like,
>     M such that (for all x,y except x=y=0) (x+y)^2+3xy isn't == 0 mod M.
>     At any rate, this Python jot produces the sequence data.
>
> #!/usr/bin/python3
> for mod in range(2,300):
>     halfmod = (mod // 2) + 1
>     for x in range(halfmod):
>         xsq = x * x
>         for y in range(max(x,1),halfmod):
>             sumsq = y * y + xsq
>             xy3 = x * y * 3
>             val = (sumsq + xy3) % mod
>             if val == 0: break
>             val = (sumsq - xy3) % mod
>             if val == 0: break
>         if val == 0: break
>     if val != 0: print(mod)
>
>
> > %C Prime numbers of this sequence are congruent to {2,3} modulo 5.
>
>     BTW, that formula equals (x^2 + 5xy + y^2);
>     that may be why modulo 5 matters.
>
> --
> Don Reble  djr at nk.ca
>
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>

```