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

Richard Guy rkg at cpsc.ucalgary.ca
Thu Feb 24 20:32:58 CET 2011

```Perhaps this sequence should start with

A000012 (n=1) has period 1 ??  or should it be
A000004 (n=1) has period 1 ??      R.

On Thu, 24 Feb 2011, Charles Greathouse wrote:

> 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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```