[seqfan] Re: Guided browsing of the OEIS based upon personal preferences?
Alonso Del Arte
alonso.delarte at gmail.com
Mon Oct 26 02:56:06 CET 2009
It's a very interesting idea and I'm sure a good portion of users would
enjoy such an interface. Probably, those who like Pandora to explore music
would also like a Pandora-like UI to explore integer sequences.
Me, personally, I prefer to explore music by reading essays and books about
music I already like and following leads I find in those essays and books. I
discovered Robert Simpson's music when I read an "About the Author" blurb
that mentioned he's written his own Symphonies in addition to writing about
Symphonies written by others.
Roughly analogously, I explore integer sequences by calculating a few terms
and looking them up in the OEIS. If I get too many results, I just calculate
a few more terms; 99% of the time I find precisely the sequence I was
looking for as well as interesting related sequences. Sometimes I use words,
such as "divisor" or "Moebius." The keywords are often helpful.
Just my two cents.
Al
On Sun, Oct 25, 2009 at 2:53 PM, Antti Karttunen
<antti.karttunen at gmail.com>wrote:
> (Note: in my previous answer to Rick, some of my own comments
> are shown as original quoted comments from Rick. My apologies,
> it's just me messing up the reply in the Gmail's composition window).
>
>
> But back to the classification of the sequences:
> in my view, the most fundamental classification of the sequences
> is based on their motivating semantics. Whether the foremost
> goal was to play with the formula, to find certain kind of numbers or to
> count something.
>
> Note that these are not necessarily disjoint categories:
>
> a) sequences with a known "easy" formula, (e.g. recurrence or a generating
> function).
> Archetypal example: Fibonacci numbers, A000045.
>
> b) sequences which count something (e.g. stable configurations of bricks).
> These often have an "easy" formula, at least after somebody finds it, in
> which
> case they also belong to (a).
> Archetypal example: Fibonacci numbers again, A000045.
>
> Sometimes no such formula is found
> (like e.g. for http://www.research.att.com/~njas/sequences/A000577 )
> thus the cases must be actually _counted_. (Manually or by computer
> program.)
>
> Now I wonder, was the original intended usage for "easy" and "hard"
> keywords
> to make this distinction clear? And BTW, A000001 has no "hard" keyword!
> Why?
>
>
> c) sequences where membership is determined by some criteria.
> Archetypal example: Prime numbers, A000040.
>
> Note that in case a) we can be sure that the sequence is infinite
> (provided the formula doesn't go singular/non-integral with some n),
> and also with b) it is certain (if the definition of structures to be
> counted
> does not allow extending it to the infinite sizes, then the rest of terms
> are simply zero).
>
> However, with c) we are in general not even sure whether
> the sequence is infinite.
>
> Now, of course one can argue that a computer program
> for counting some structures or finding integers with
> some criteria is also a "formula", and indeed it is,
> and in the case of primes it is even a primitive recursive function
> (but this hinges on Bertrand's postulate, if I remember
> my Math.Log. courses correctly)
> But one has to draw a line somewhere?
>
> I wonder whether the concepts from the theory of computation
> would actually make this any more practical?
>
> And where do the general "sieve-type" sequences fit, (c) I guess?
>
>
> Again, random two cents from,
>
> Antti
>
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