Primefree sequences in the OEIS. A bad idea.

[Alexandre Wajnberg]

>>>> Yes but has OEIS the unique goal to be a tool useful to a researcher?
>>>> This is the most important one of course.
 
>>> I agree, the OEIS is not exclusively a research tool.
>>> (...)  And remember that other literature references the OEIS as a learned
>>> resource.

I would add (as I said to David in a separate mail) another "raison d'être"
for OEIS worth to be taken in consideration: popularization of number theory
(or aspects of it) through "special" or "original" sequences (sequences
which are funny, or which excite the imagination of the "readers", or which
can be linked to chapters of the History of maths...)
These parts of OEIS are nice doors (as didactic resource and as "play
ground") to enter into the world of numbers.
This is a reason (among others) for accepting sequences not exclusively
"pure maths".

Concerning the sequences describing physical objects (e.g. astronomic
parameters), biological realities ( e.g. genetic code), human constructions
(e.g. different measures of time), human creations (Beethoven fifth
symphony), etc... which I think are interesting ones, David answers:
Yep, limited forays into such areas are interesting.  On the other hand, we
could fill the OEIS with encodings of music, words, chemicals, etc, and I
don't think this is the point of the OEIS.

I agree, OEIS has not to be the total numeric description of the Universe...
Although this is a delicate problem at second glance.
If we consider (from a platonician point of vue) a very existence of
mathematical objects (wether created or not by human being), why then
discard sequences differently "ruled" (than by math) but which are
describing real stuff, solid human ‹ or not ‹ reality?!
Difficult to put the threshold... It's a matter of the "linkability to
maths" of the objects involved: <symmetries of a cristal> is closer to maths
than <number of stars having magnitudes n present in the Smith catalogue>.

May be a key word <non math> for such sequences? (I don't know if it is
possible to add one; if not, in a C line?)


>>> Clearly, this purpose [OEIS as a learned resource] has been gradually
relaxed over time.  The database started to include interesting sequences that
were not referenced in the literature, e.g, recreational sequences. When the
OEIS came along, and the general public was allowed to submit, the volume of
sequences increased and quality fell.

OK, this causes more work and complications for the maintainers of the base,
but on the other hand, this "falling of quality" has to be relativised: for
the user, whatever the size of the data base, it takes quasi the same time
to look up a sequence; other sequences, irrelevant or not, stay invisible
(except if they share the same substring, which has a low probability to
occur).

A (weak) positive aspect of the acceptance of game and amateur sequences is
that it connects different ways of thinking, with possible heuristic
consequences. Amateurs "are downstairs" but some of them may bring
interesting stuff. They constitute also links between world of maths and the
society in general.

Again, where to place a limit (and following which criteria) between
interesting and not ‹ sequences?
At least, (quasi) *exhaustivity* is a logic rule (exhausting rule!).

 
> I have always contended that (...) new sequences should be reviewed by
> at least two editors, who are able to admit or reject a sequence based on
> accuracy, completeness and relevancy.  The downside of this is that it might
> discourage amateur submissions, though I haven't decided if this is a good
> or bad thing.

Yes (I think "good" amateurs will not be discouraged).
At least we could begin with a simple mesure: to make a point, sort of "good
practice" document, with numerous exemples of "not really interesting"
sequences. It would be useful for some seqfans and newcomers. (we all
noticed that the semi-volontary moratorium was quite well respected by us,
and we may expect the same thing for a volontary attention to the relevance
of the new sequences, if this is clearly required.)


> Ultimately, we have to see the existing database as a database, without
> regard to quality or relevance.

Yes. Why not...


> In the past, NJAS has published his database twice in book form, as the
"Handbook of Integer Sequences" and the "Encyclopedia of Integer Sequences".  In
each case, NJAS did not publish all of the sequences in the database, but a
subset of relevant sequences.
> This indicates to me that a good portion of the database is not up to
> publication standards.

Yes, good deduction; I see it otherwise: for commercial reasons a book has a
limited number of pages and choices have to be made... (two or three
"bonaccis" are enough!)


> So a better solution to this problem might be to put a review process
> between the existing database and a new database of publication-quality
sequences. This method could also be used to change the format of the database.

Tough work! 
And what about a sort of key word <Research sequence>? (sorry to re-propose
this kind of hard job).
Or a two floors database? (Anyway it would re-require criteria to range the
sequences... Then a reviewing process by editors. More work ultimately.)


THUS IN SHORT: 
  because
‹ OEIS may also be a tool for popularization of number theory,
‹ the "falling of quality" of OEIS doesn't seem to appear to the user,
‹ amateur and game sequences may have heuristic consequences,
...so, maintaining the current opening of OEIS, but "balanced":
‹ If non math sequences are "in", to consider their "linkability" to maths?
‹ two propositions: new key words <non math> and <research>; and to publish
a "good practice" document with exemples of "not so interesting" sequences.


Alexandre



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