[seqfan] Question about Dickson ordering (see links).

Michel Marcus michel.marcus183 at gmail.com
Sat Apr 23 14:00:49 CEST 2022

Hello seqfans

Here are 2 links: https://www.jstor.org/stable/2969383  and

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);

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?


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