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

Alois Heinz heinz at hs-heilbronn.de
Thu Feb 24 20:43:09 CET 2011

```It seems that this sequence has n/a(n) = period: 1,1,1,2

Can you confirm this?

Alois

Am 24.02.2011 20:03, schrieb Charles Greathouse:
> 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

```