[seqfan] Re: Question about Dickson ordering (see links).
Michel Marcus
michel.marcus183 at gmail.com
Sat Apr 23 17:35:51 CEST 2022
Yes for 65537.
But for 17 the program gives 17 [1, 3, 8, -7, -21, -63, -189, -567].
So there must something else to do than tripling instead of doubling.
Le sam. 23 avr. 2022 à 17:15, Fred Lunnon <fred.lunnon at gmail.com> a écrit :
> << \\ here it is to take care of 17 and 257 >>
> And 65537 (etc.) perhaps? See
> https://en.wikipedia.org/wiki/Fermat_number
> Hermes' manuscript reportedly appeared in 1894 ...
> WFL
>
>
>
> On Sat, Apr 23, 2022 at 1:01 PM Michel Marcus <michel.marcus183 at gmail.com>
> wrote:
>
> > Hello seqfans
> >
> > Here are 2 links: https://www.jstor.org/stable/2969383 and
> > https://www.jstor.org/stable/2968678.
> >
> > I wrote a PARI program to give the ordering of cords.
> >
> > isp2(n) = my(m); ispower(n,,&m) && (m==2);
> > row(n) = {
> > if (n % 2,
> > my(p = (n-1)/2);
> > my(c = if (!isp2(n-1), 2, 3)); \\ here it is to take care of 17 and 257
> > (as he wrote)
> > my(k=1, v=vector(p));
> > for (i=1, p,
> > v[i] = k;
> > k *= c;
> > if (k>p, k = n-k);
> > );
> > v;
> > );
> > }
> >
> > It is not clear to me if this is supposed to be used for any n ? or for
> > odd n ?? or for n prime ???
> > So to test I only do forprime(n=3, 37, print(n, " ", row(n)))
> >
> > The output for n=13 and 19 match what we see in 1st link; and for n=37
> what
> > we see in 2nd link.
> >
> > But the method does not seem to work for n=31.
> > But the tripling method does not work for n=17 and n=257.
> >
> > Do you see how it should work for these values?
> > Thanks.
> >
> > MM
> >
> > --
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>
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