n! = a^b

Marc Le Brun mlb at well.com
Thu Sep 3 19:20:49 CEST 1998

>=Wouter Meeussen>
>I really don't know if 'best approximations' have a place in EIS.
>do you think they belong there?

NJAS is of course the final arbiter, but in my opinion the main point of
the EIS is to act as a central cross-index of knowledge about sequences, so
the criteria should be generally more, rather than less, inclusive.

I view the potential cross-indexing value as characterized by two extremes
(with any given "hit" falling somewhere within this spectrum):

  Common, mildly valuable: the "lookup" returns a reference to (some of)
the existing literature related to a sequence.  This is really helpful when
you've simply stumbled across some previously studied sequence, and so can
thereby gain entre into the wider mathematical knowledge base about it.

  Uncommon, wildly valuable: the "lookup" reveals some unexpected
explanation or connection with other sequences.  This is the big payoff,
where the EIS contributes directly by actually extending the sphere of
known mathematics.

Of course I mean "lookup" here in the sense of superseeker (versus a simple
literal lookup) where the query sequence is used to generate some "cloud"
of "neighbor" sequences to be compared to those stored in the database.

I think the probable impact on future cross-index lookups should form the
main basis for judging whether to submit or prune a given sequence.  You
can ask two simple diagnostic questions:

1. Is this sequence likely to get "hit" automatically anyway, because it's
in the "cloud" surrounding an existing sequence?  Some transforms of known
sequences may fall in this class.  (Sometimes I include in this criteria
"neighbor" sequences which superseeker may not be able to detect today, but
would plausibly be found by near future technology).

2. Is the provenance of this sequence so obscure that it's extremely
unlikely to ever arise in any future query?  Some sequences which are lone,
undistinguished, points in large spaces (eg the space of outputs of
extremely complicated numerical programs with lots of parameters) may fall
in this class.

On the other hand, as I said, I think it's better to have more rather than
less.  When I find any sequence with a simple or fundamental description,
or which is somehow uniquely distinguished, then I try to make sure to
submit it, even if it seems pretty trivial, because I think it's important
for the EIS to contain such things in its "basis set", to increase the
likelyhood that some interesting new connection might be hit on in the future.

Unless NJAS says otherwise, I wouldn't worry too much about overloading the
EIS with too many sequences.  It's a "surety" that computational power and
storage capacity will grow faster than our ability to invent plausible
candidate sequences, even with very weak selection criteria.

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