[seqfan] Re: Periodicity of seqs mod m - research idea

Neil Sloane njasloane at gmail.com
Sun Feb 19 03:03:21 CET 2017


Harvey said:  "a new function in Mathematica version 10 is
FindTransientRepeat."
This worries me. Without independent verification I would not accept the
results of a secret program like that. Especially if their program says
there are no cycles.
What method do they use? Is it probabilistic or deterministic? Certainly if
they claim to find a cycle that can be checked but one would still need to
check that there is no shorter cycle and that their cycle does not begin
any earlier than they claim.

I wrote a Fortran implementation of Floyd's algorithm in 2010 that I would
be happy to send anyone. It is quite short. There is also a C translation.

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Sat, Feb 18, 2017 at 5:59 PM, Harvey P. Dale <hpd at hpdale.org> wrote:

>         A fairly new function in Mathematica version 10 is
> FindTransientRepeat. For folks using Mathematica, employing that function
> may assist in identifying periodic cycles.
>         Best,
>         Harvey
>
>
> -----Original Message-----
> From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Marc
> LeBrun
> Sent: Saturday, February 18, 2017 3:23 PM
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Subject: [seqfan] Re: Periodicity of seqs mod m - research idea
>
> On Feb 18, 2017, at 11:44 AM, Neil Sloane <njasloane at gmail.com> wrote:
>
> > To test for the presence of a cycle (which in general won't start at
> > the beginning of the sequence) the standard alg. is Floyd's hare and
> > tortoise alg.  There is a Wikipedia article on Cycle Detection.
>
> In some situations Gosper’s algorithm (cited but not described in
> Wikipedia) is nice http://www.inwap.com/pdp10/hbaker/hakmem/flows.html
> ITEM 132 (Gosper): LOOP DETECTOR
>
>
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