[seqfan] Re: Sowing integers

[Max Alekseyev]

Having smaller loop is not possible. If we have certain sequence of
integers and a position s where next sowing starts, then we can
uniquely identify the previous sequence (i.e., each sequence/position
under sowing mapping has not only an unique image but also an unique
pre-image, and therefore belongs to some loop).

Namely, the position where the previous sowing started is the one with
the smallest integer in the sequence and (cyclicly) rightmost closest
to s (possibly s itself) if there are several smallest integers in the
sequence.

For example, sequence 5,4,3,7,3,5 with the sowing position at the
integer 4 implies that the previous sowing started at where the
rightmost integer 3 is currently located and was applied the sequence
1,0,0,4,21,1.

Regards,
Max


On Wed, Sep 12, 2012 at 12:49 AM, David Scambler <dscambler at bmm.com> wrote:
>
>> Maximilian wrote: " whether (or why) there cannot be some smaller "loop"
>> in the orbit of some numbers such that the initial position would
>> never be reproduced"
>
> Indeed. I have unsuccessfully searched for short orbits in integers up to 1 million.
> I am not sure when to stop searching and conjecture instead that there are none.
>
> The longest loop so far is 223200 for the integer 98999. Perhaps someone can check this assertion.
>
> dave
>
>
>
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