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

[Charles Greathouse]

The good news is that since he OEIS already handles constants on input
(it knows that 3.14159 means it should search for 3,1,4,1,5,9) and we
already have keyword:cons for constants, it's entirely possible to
build those better constant-recognizing tools into the OEIS.  Of
course we can also integrate with other projects.

Features that would be nice for constant searches would be restricting
searches to start at the left, checking offsets*, equating forms with
different offsets and numbers of initial zeros, and checking continued
fractions.

* This requires that the offsets themselves are correct!  Some years
ago this was a real problem; I think that editorial work since has
much improved this.  But until some feature actually uses it
extensively it's hard to say.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Thu, Sep 8, 2011 at 9:35 PM, RGWv <rgwv at rgwv.com> wrote:
> Marc,
>
>   The Plouffe Inverter is still there. see http://pi.lacim.uqam.ca/eng/
>
>   We all make mistakes. Yes, some of us get defensive but the integrity of
> the OEIS is at stake. Once that is lost then why bother. I for one am
> checking out a b text file for errors which Tony pointed out to me. Although
> this is requiring a week of CPU time, it is necessary to eliminate the
> problem which Tony pointed out. Suck it up and do the job accurately.
>
>   If there is a resource which would houses the "Constants" which the OEIS
> has then I see the merit of segregating the integer sequences from the
> decimal expansions. But at present, that resource did not exist. At least
> not to the depth that the OTIS does. Maybe the OTIS should "spin off" the
> later?
>
> Sincerely yours, Bob.
>
> -----Original Message----- From: Marc LeBrun
> Sent: Thursday, September 08, 2011 7:35 PM
> To: Sequence Fanatics Discussion list
> Subject: [seqfan] Re: [math-fun] about 10000 numbers, a certain document
> from M.I. Shamos.
>
> 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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>>>
>>
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>
>
>
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