[seqfan] Re: Guided browsing of the OEIS based upon personal preferences?
Rick Shepherd
rlshepherd2 at gmail.com
Mon Oct 26 18:08:36 CET 2009
Antti (and others),
Please see my comments below; look for "Rick again". (It seems that the
shelf-life of a GRE score is
somewhat < 33 years; as a result, I'll be busy until later in the week:
There are those verbal -- and
now -- writing sections!).
On Sun, Oct 25, 2009 at 2:13 PM, Antti Karttunen
<antti.karttunen at gmail.com>wrote:
> On Sun, Oct 25, 2009 at 18:06, Rick Shepherd <rlshepherd2 at gmail.com>
> wrote:
>
> > ...and thanks for your comments!
> >
> > I *shouldn't* really spend the time right now to respond with the detail
> > your comments deserve -- but I do want to make a few, quick points:
> > 1) I've also thought that this group might want to spend time discussing
> > potential new keywords (or, as you now say, categories -- although I'll
> > probably use the terms interchangeably below), at least for manual
> > attachment to entries. I'm sure that different people have different
> > interests and needs here -- and that other people should have much more
> say
> > than me on this.
> >
> >
> It would be great if there would be a talk-page in new OEIS Wiki for that,
> something like Talk:Ideas for new categorization.
>
> Rick again: This makes sense to me too, including beginning with
brainstorming
all ideas that could conceivably be useful to anyone, doing "meta-analysis"
of
the relationships of the proposed categories to each other (figuring out
all the
implied category inclusions including with existing keywords), rejecting
what
turn out to be duplicate (or very-nearly-so) categories, selecting a
workable
group of the categories -- all while keeping in mind that they can be
useful
not only for manual searches but also for metrics for (optional, depending
upon user and circumstances) inclusion in Robert Munafo's Pandora-like UI
interface.
<Rick snipped some for brevity>
> 4) Several months ago, I stumbled upon "PersonalBrain" software at
> > www.TheBrain.com <http://www.thebrain.com/> <http://www.thebrain.com/>.
> <... snipped ...>
> > I may be able to show a picture
> > of one of these screens but I know I shouldn't put it here in this
> list.).
> >
> > You can mail it to me, I can then make it available under my home pages.
>
> Rick again: I can e-mail you some screenshots later this week.
>
> > 5) Some other possible categories (not all of equal importance and some
> > implying others or existing keywords; some may overlap or be identical to
> > yours, I don't have time to check right now):
> > all terms are constant
> > alternating signs
> > each term appears a finite number of times
> > each term appears an infinite number of times
> >
> >
>
> > each term is composite
> > each term is prime
> >
> > These are just specific cases of more general way classify a sequence:
> each term occurs in the sequence (viewed as a set) Axxxxxx, in these cases
> A002808 and A000041.
>
> non-increasing (vs strictly decreasing)
> > non-decreasing (vs strictly increasing)
> >
> > I.e. whether the first differences contain zero or not.
> I think it would be quite expressive if various transforms could be used
> in the category-definitions.
>
>
> > all terms are bounded above
> > all terms are bounded below
> >
> >
>
> > terms based upon words of language XYZ
> >
> > I thought the keyword "word" is just for that, or not?
>
> Rick again: I'm suggesting something like enhancing the keyword "word"
to "word:German". In general, I'd suggest allowing parameters to many
keywords (if feasible) to ease searching; this could also cover cases as
above
where you pointed out that we could generalize to "all terms in this
sequence
are in Axxxxxx" -- and other cases below and mentioned elsewhere. Doing
this constrains/simplifies the syntax of how searches need to be done -- and
would, hopefully, eventually once completely in place, ensure more complete
matching.
(Perhaps the "German" example above is not as immediately convincing as
others would be
because we can already do "keyword:word German" as a search -- but this also
matches "German" anywhere else in the entry if it happens to be there).
> > parity is odd
> > parity is even
> >
> >
> These are just specific cases of a rule Axxxxxx(a(n)) = Ayyyyyy(n).
> In this case, for parity is odd: A000035(a(n)) = A000012(n),
> and for parity is even: A000035(a(n)) = A000004(n).
>
> Another very generic rule: a(Axxxxxx(n)) = Ayyyyyy(n).
> (Tentative cases could also be collected now and then by
> the bot, although I'm afraid this would generate a huge
> number of conjectures nobody wants to prove!)
>
>
> > (more generally) all terms are congruent to j mod k
> > (maybe even) terms have same number of digits
> >
> > Again,
> A055642(a(n)) = ...
>
> Rick again: The sky's the limit! Good suggestions. One keyword tag could
> conceivably be "Big-oh(Axxxxxx)" and similar, to follow-up on others'
> rate-of-growth interest.
>
Also, periodic:n, where n is the period could be useful (before I forget
again.). There's probably
a routine out there already that could easily determine the (likely)
period from given terms.
Regards, Rick
<other things snipped>
> Yours,
>
> Antti
>
>
>
>
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