[seqfan] Re: Period lengths of k^2 mod n not in OEIS ?

Charles Greathouse charles.greathouse at case.edu
Thu Feb 24 20:03:51 CET 2011

```I concur with your results.  (I read as little of your post as
possible and wrote my own code to minimize the chance of sharing an
error.)

You should certainly submit this!  It's worth mentioning that a(n) is
a multiple of A019554(n).

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Thu, Feb 24, 2011 at 1:30 PM, Richard Mathar
<mathar at strw.leidenuniv.nl> wrote:
>
> In conjunction with A182865 the following topic arose:
>
> The sequence k^2 mod n for some fixed n has a period length not larger
> than n (that is fundamental, k^2 is a polynomial...).
> Examples:
> A000035 (n=2) had period 2,
> A011655 (n=3) had period 3,
> A000035 (again, n=4) has period 2,
> A070430 (n=5) has period 5,
> A070431 (n=6) has period 6,
> A053879 (n=7) has period 7,
> A070432 (n=8) has period 4,
> A070433 (n=9) has period 9,
> A008959 (n=10) has period 10,
> A070434 (n=11) has period 11,
> A070435, A070516 (n=12) has period 6
> The number of different members in the period (set size of the moduli)
> is A000224(n).
>
> Now the strange thing is that these period lengths,
> 2,3,2,5,6,7,4,9,10,11,6,...
> seem not to be in the OEIS -- although they look even more fundamental than
> the Pisano periods in my eyes. Am I fumbling somewhere here ?
>
> Richard Mathar
>
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