[seqfan] Re: My page on the Wiki for detected relations between sequences
Neil Sloane
njasloane at gmail.com
Sat Dec 23 20:57:10 CET 2017
This is the ancient question of "if two sequences agree for K terms, must
they be the same?"
and there are examples in the OEIS of pairs of sequences which first differ
after
thousands of terms, or millions of terms, and in one case 10^15 terms.
There is an entry in the OEIS Index for
(IIRC) "sequences which agree for a long time but are different"
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, Dec 23, 2017 at 2:02 PM, Antti Karttunen <antti.karttunen at gmail.com>
wrote:
> On Sat, Dec 23, 2017 at 12:31 AM, <seqfan-request at list.seqfan.eu> wrote:
>
> > ------------------------------
> >
> > Message: 18
> > Date: Thu, 21 Dec 2017 10:59:31 -0400
> > From: "M. F. Hasler" <seqfan at hasler.fr>
> > To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> > Subject: [seqfan] Re: My page on the Wiki for detected relations
> > between sequences
> > Message-ID:
> > <CABxCbJ1DoCCt_ESMYuLQHzFfZEy-y=2j8BVRZDbtcjp=W_pCVg at mail.
> gmail.com>
> > Content-Type: text/plain; charset="UTF-8"
> >
> > On Dec 19, 2017 9:03 AM, "Thomas Baruchel" wrote:
> >>
> >> On Tue, 18 Dec 2017, Robert Israel wrote:
> >>> This may be a rather unfortunate example to start with
> >>> (or perhaps we should say, it nicely illustrates the pitfalls
> >>> of these algorithms). It is
> >>
> >>
> >> Yes, I removed this example;
> >> this is the purpose of this list;
> >
> > IMHO it might be at least as interesting to list the false positives, as
> > well as the true relations.
> > (I imagine something like "The apparent relation Axxx +- ... = Azzz is no
> > more true beyond n = ...) -- just like the helpful remark Robert has
> > pointed out.
>
> I would be very interested to know what are some of the values of n
> for such cases where it could be first seen that a conjecture proposed
> by Mr. Baruchel's program turned out to be false. That is, cases where
> the amount of terms in stripped.gz (in the data-section of each
> sequence) would have indicated the relation holds, but when checking
> beyond that (with the data from the b-file or by computing the terms),
> it turned out to be false. There's also a point that stripped.gz
> doesn't tell the starting offset of the sequence (and in any case it
> might be "wrong"), so one might need to try several alignment shifts
> between the sequences?
>
> In my own "OEIS Djinn" datamining project, I have noticed that for
> some cases this "refutation point" (where it will turn out that A(n) =
> f(B(n)) cannot be true after all) might go even up to a few thousands.
> Thus the need to work with data given in b-files, and creating and
> submitting such b-files if not already provided. As long as we have no
> any established syntax or "ontology" in place for clearly indicating
> such refutations (that is, machine-readably), it is better to have the
> program figure that by itself, from the data alone.
>
>
> Best regards,
>
> Antti
>
>
> >
> > Cheers,
> > Maximilian
> >
> >
>
> --
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>
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