[seqfan] Re: [math-fun] about 10000 numbers, a certain document from M.I. Shamos.

Marc LeBrun mlb at well.com
Fri Sep 9 01:35:42 CEST 2011

I have to admit I've always been a bit uneasy with the OEIS entries that
give the digits in a "decimal encryption" (as Bill Gosper calls them).

First it's always seemed that they really deserve their own database (um,
whatever happened to "Plouffe's Inverter"?) that better-respects their true
nature as decimal expansions.

Another characteristic feature of this data set, not shared by general OEIS
entries, is the tight binding between the "unique keys" (ie numbers) and
their associated formulas, which are given in a canonical language.

Either way, a nice potential feature might be an ability to search on the
formulas--say for all expressions involving both pi and e.

A few other concerns:

  *  The accuracy of all digits in such entries should be perfect.  The OEIS
isn't really well-suited to support concepts of "approximate sequence",
whereas one expects floating point values to have "fuzz".

  *  And of course the formulas shouldn't be buggy--yet already folks have
pointed out errors in this data set.

Given these issues I would suggest that rather than blindly uploading the
dataset any assimilation be conducted as a systematic project that includes
mechanically "compiling" all the formulas and testing (when feasible) the
deviance from the values given (presumably producing a bonepile for further
editorial inspection).

Another thing to evaluate before proceeding would be potential impact on
things like superseeker (and its far-future descendants, who I think will
ultimately be the majority of the OEIS's user base!).  Lists of digits are
reasonable targets for direct simple lookups, but they'll mostly just be
noise with respect to Mobius transforms, or the like.

The 10K new sequences would constitute about 5% of the current OEIS entries.
I suppose that might be a tolerable incremental load, both for superseeker
and false positives, but what should the policy be in the future if someone
generates enough to become 50% of the OEIS, or more?

Lastly, returning to the formula data, another more "traditional" way to
augment the OEIS might be to sift through the formulas (mechanically I
presume) and somehow determine if they implicitly incorporate integer
sequences, such as for various flavors of generating functions.  These could
be automatically cross-checked against the OEIS and added if new, and the
entries supplemented not only with numerical values but also with
references, additional formulas, and so forth.

>="Simon Plouffe" <simon.plouffe at gmail.com>

> No,
>   as a real number : like the other known constants
> of interest, like pi, 3,1,4,1,5,9,2,6,5,3,5...
>   there is also the possibility of having the continued
> fraction as well, if it is of interest of course or if
> someone suspects that it could have one.
>   bonne soirée, have a nice evening,
>   Simon Plouffe
> Le 08/sept./2011 19:23, Adam P. Goucher a écrit :
>>> Neil, would you agree that we should include these entries into the
>>> OEIS ?
>> As what? Continued fraction expansions?
>> Sincerely,
>>        Adam P. Goucher
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