[seqfan] Re: Guided browsing of the OEIS based upon personal preferences?
antti.karttunen at gmail.com
Sun Oct 25 19:13:01 CET 2009
On Sun, Oct 25, 2009 at 18:06, Rick Shepherd <rlshepherd2 at gmail.com>
> ...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.
> 2) To agree with you at least on the need for a "non-" descriptor for
> keywords: Currently, for example, there is "fini" and absence of "fini"
> which doesn't necessarily imply infinite, so there should at least be an
> equally clear way to designate that a specific sequence is known to be
I think the basic set of keywords without "non-" attribute should all (or
most) apply to
the properties which can be only conjectured by the bot, and their
(prefixed with "non-") to properties which can be proven by finding even
a single counter-example. So, instead of "sign", we would say "non-nonn".
But of course this doesn't yet tell whether we should have "fini" and
or "infn" and "non-infn"!
> I need to think longer about such things as "conj-", "unkn-", or
> "bot-" (and/or even "bot-conj-") in a similar context.
> "botconj-" sounds nice. "conj-" would be then preserved
conjectured made by some conscious human being.
> 3) I've spent several days earlier this year thinking of other ways (perhaps
> non-traditional) of classifying sequences. I'll list a few below (in 5).
> 4) Several months ago, I stumbled upon "PersonalBrain" software at
> 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.
> 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?
> 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
A055642(a(n)) = ...
(maybe even) terms are all base n digits
> etc., etc.
> [Of course, with text searches available there are alternate ways of doing
> this -- but to make searching easier agreed-upon and enforced methods would
> be necessary]
> I think you've definitely helped start a discussion worth having.
You started it... !
> P.S. I didn't address your comments in "B" about analogues -- but this
> would be a very valuable feature certainly (but also requiring more manual
> P.P.S. I see that Franklin's just posted a message but I haven't read
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