[seqfan] Re: Question about Dickson ordering (see links).
Fred Lunnon
fred.lunnon at gmail.com
Sat Apr 23 17:15:22 CEST 2022
<< \\ 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
>
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>
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