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Summary of Suggestions Concerning OEIS From OEIS_50 Workshop

N. J. A. Sloane and others
October 16, 2014; edited for OEIS Wiki, Oct 25 2014

A workshop on "Challenges of Identifying Integer Sequences" was held at the DIMACS Institute, Rutgers University, October 9 and 10, 2014

The following is a list of suggestions that were made at the meeting or arose during discussions prompted by the meeting. With over 110 participants, there were naturally a lot of suggestions.

Suggestions for improving Superseeker

The first topic is especially relevant since it is directly concerned with the stated theme of the workshop.

Add a k-regular sequence recognizer [Jeffrey Shallit] Also a k-automatic sequence recognizer, at least for the common special cases k = 2 or 10. [Charles Greathouse]

Upgrade the Mathematica code used by Superseeker. In /home/oeis/bin, there is a Mathematica file seqtranslib.m . [Olivier Gerard suggested this and offered to do it]

Looking at the Superseeker log file shows that there are a number of error messages from Maple. Whatever is causing them needs to be fixed! These were messages like "maple: fatal error: lost connection to kernel", if I recall correctly. See the file /log/mail_superlog, circa lines 215552, 488788, etc. [Olivier Gerard and Neil Sloane]

Need to adjust the parameters in gfun so that it searches for recurrences etc. of higher order than the default values give you. [Neil Sloane]

Superseeker should be modified to handle triangles of numbers (in the regular triangle, tabl, format). It could see if the triangle matches an existing triangle, and if so, report this in a nicely formatted way. If the sequence appears to be a new triangle, try to identify it with special triangle-matching programs.
Is is it a Riordan array?
Is it the transpose of a triangle that we have?
Is it an existing triangle with an outer diagonal removed or added?
Etc. [Reinhard Zumkeller and Neil Sloane]

It was mentioned that SuperSeeker could provide the means for a requester to follow up with data about which results were or were not useful, to gather data that might eventually help tune its algorithms. [Hugo van der Sanden and Charles Greathouse]

Looking for linear combinations in Superseeker

How to look hard for sequence combinations?
Neil must have addressed this in Superseeker, but I haven't seen any write-up.
Suppose I have generated a new sequence M(n), and it's not in OEIS. Maybe it's some combination of OEIS sequences. What's a good way to proceed?
I can look for M(n) = A(n) + B(n) reasonably efficiently (assuming I have a local copy), but trying A+B+C etc. rapidly outruns available computing resources. Also, automatically rejecting false positives looks hard. This seems like a natural area for research. [Rich Schroeppel]

An early version of Superseeker did try to find a match with a linear combination of two sequences. It looked at c*A(n) + d*B(n+n_0), and tried small values of c,d,n_0 and all pairs A,B from the database. The trouble was, it was slow, it found a lot of false matches, and IIRC it never found anything useful. So I dropped it.
It is certainly a project worth doing off-line though. Take all triples A, B, C of sequences and see if there is a linear dependence among them. To cut down on trivial matches, restrict A to be a sequence that has no known formula. Although the hard part would be to decide if a positive result was a known identity (which it would be most of the time) or a new discovery. [Neil Sloane]

Note: Yangchen Pan and Max Alekseyev had a poster at the conference which gave heuristics for filtering out trivial matches and determining if identities were known. [Charles Greathouse]

Neil, I'm imagining a button on the search page that asks the user if he wants to look for combinations, but clearly you've got to keep the compute cost down. The 'slow' part can be partially addressed with a clever algorithm.
If you want to see if A[n] = B[n] + C[n], sort the data set on X[1], and scan through the values A[1]-X[1] looking for a match with the reverse-sorted X'[1]s. For your case below, with unknown TBD coefficients c and d, looking for a cross-ratio coincidence between (A1 B3 - A3 B1) / (A1 B2 - A2 B1) and (A1 C3 - A3 C1) / (A1 C2 - A2 C1) would find candidate B,C pairs. The false-positive problem might be addressable when more terms of A are available -- analogous to the real-number version of the problem where we just compute a few more decimals.
The "Nothing Useful" problem is more serious -- it says the cost of finding for a new discovery is very high, and not just compute cycles, but research effort. Perhaps Euler's zeta2 = pi^2/6 was the only time the cost/benefit ratio was favorable.
A look into what you've tried with Superseeker would be interesting. [Rich Schroeppel]

Superseeker is an email service, and we stack up the jobs as they come in and process them in (you guessed it) the order in which they were received.There are a bunch of other tests that we could do,
- including ones like the one you mentioned -
- and there are a lot of others I've collected in my notebooks over the years
- one was called [something in German which sounds exactly like Mozart]
- and several others
and we could have a supersuperseeker program to run them. Another thing we could do is adjust the parameters of guessgf (guess generating function, the very best thing in the world and part of Maple's gfun package) to try harder - to look for higher degree generating functions.
Supersuperseeker should have different constraints on how it runs
- we would allow it more time to think,
- we would strenuously try to repel robots and undesirable humans, in fact you might need to ask for special permission before you could use it
This is something that we all might try to work on once the conference is over. [Neil Sloane]

My main reason for the remarks was to try to drum up some interest from the group to look for more methods to look for combiners cheaply. Some of the subscribers to the list are very creative. [Rich Schroeppel]

Just in case anyone is interested, I had a master's student (Peter Liu) look into this very question some time ago. We developed some techniques that could speed up questions like: is a given sequence the linear combination of two sequences in the table? But I do not know any way to do this for more than two sequences in a reasonable length of time.
You can see my master's student essay here:
https://cs.uwaterloo.ca/~shallit/peter-liu-masters.pdf [Jeff Shallit]

Peter Liu's algorithms -- especially #6, the modular methods for linear combinations -- would be worth considering for Superseeker. [Charles Greathouse]

General remarks about making changes to the OEIS

Before any change to the OEIS is made, I suggest that careful thought be given to the possible negatives of that change - especially negative effects on the people who use the database in any capacity. An easy principle for people to forget, especially when a lot of changes are being proposed at once - now, for instance.

Also, in most cases it's good to announce the OEIS change on SeqFan, and/or update the style guide, and/or document the change in whatever other way may be appropriate, in a clear and accurate way. (I think this is done more often now than a few years ago, and I appreciate the increased user-friendliness!)

And ideally, whoever announces an OEIS change will take the time to understand what the old way of doing things was. This can make a difference in whether or not the change is announced clearly and accurately. [Matthew Vandermast]

Suggestions for improving the web interface

The web interface definitely needs an upgrade to HTML5, with an eye toward better displays on portable devices. I intend to take a crack at this when my queue clears up a bit. [William Cheswick] David Desimone said he would be interested in helping with this project - giving the OEIS web pages a "fresh coat of paint" [Neil Sloane, Oct 17, 2014]

Russ might add programming to the web site to improve the spacing in Mathematica programs automatically so they fit more nicely into that field. [Harvey Dale, Oct 13 2014]

Add some new keywords that will make it possible to display irregular triangles, in the same way that keyword "tabl" is a link to show a regular triangle. The two main irregular triangles have rows of lengths 1,3,5,7,9,11,..., and 1,1,2,3,4,5,6,7,8,... These might get keywords tabA, tabB, say. Are there other irregular shapes that are important enough to get their own keyword? [Olivier Gerard and Neil Sloane]
It has been proposed in the past (sorry, I don't remember who brought this up) to have the ability to index tow lengths by an arbitrary sequence, so tabl, tabA, tabB would become tabl(A27), tabl(A5408), and tabl(A028310) respectively. I think the proposal has merit, and it shouldn't be hard to implement (we could even special-case those three so as to avoid common lookups). [Charles Greathouse] I discussed the idea of having keyword tabl(A5408) (say) with Olivier, and it seemed clear that this would be much more complicated. If we restrict to 2 or 3 fixed formats then the programs can be changed very easily. Allowing arbitrary lengths for the rows would be a nasty formatting problem. [Neil Sloane]

Maybe you refer to my suggestions of Keywords with parameters, Charles (and Max Alexseyev, IIRC) also contributed to this idea. It would yield at once several different improvements: not only tabf(Axxx,o), but also frac(Axxx,n/d), and maybe most interesting, lrec(c1,...,cN).
The latter provides an example of dynamic content, and allows to compute variable b-files. [Maximilian Hasler]

We might consider an optional field called "Theorems". (Regarding a new database of theorems, as proposed by Sara Billey, my thought was that, given OEIS.org and MathWorld and Wikipedia already exist, a separate DB of theorems might be a little over the top.) OEIS is great in that users search for (sub)sequences of numbers, which ensures that search requests are language- and culture-independent. If, instead, the prevailing scenarios were to search for, say, a theorem's "proper name", that might result in unnecessary ambiguity. (One example: for US school kids, "Thales theorem" is about inscribed angles, while for Russian school kids "Thales theorem" is about parallel lines cutting proportional segments on angle sides. Such verbal searches are intrinsically culture-dependent.)
However, a nice-to-have future feature in OEIS.org may be an additional, optional, "THEOREMS" section along with the existing COMMENTS, FORMULA, and REFERENCES. Still, even the existing fields, particularly FORMULA and COMMENTS sections do a good job already, in terms of identifying the relevant theorem(s). [Alexei Kourbatov]

Concerning the underlying code that runs the OEIS: there was some discussion of succession planning for the code that runs OEIS - Charles mentioned he'd been learning Go for the purpose of understanding the code; but we really need Russ to get it into shape and document it. [Hugo van der Sanden]

There was some discussion (and a poster, from Eric Rowland) about the value of semantic tagging, so that software could better understand what parts of the sequence data it could deal with automatically.
I don't remember any specific conclusions: there's a desire to make the way we express things like formulae and (say) Mathematica code be more regular; but there probably also needs to be additional metadata that indicates that it _is_ regular. I think that means having one of:
- add keywords, such as "formula_is_regular";
- add a new type of metadata (similar to but distinct from keywords); that might be more explicitly intended for consumption by computers, and would not need to be shown by default on the web page for the sequence;
- copy content of generic fields into more specific fields to represent something verified as regular.
It was also mentioned that not all conjectured formulae are clearly marked as conjectures - I think you said Simon Plouffe added many of these. [Hugo van der Sanden]

It would be nice if the formulas were written in the Zentralblatt uniform style, so they can be searched and indexed. [Joerg Arndt] There is also MathML, MathJax, etc. Whichever format we choose, the formulas should also be written in "human" language - we need both versions - that is, we want to see the formulas written with sin(x), Sum_{i=0..n}, etc., as well a version with a lot of extraneous formatting characters. [Neil Sloane]

The poster I presented at the poster session suggested storing some OEIS data (namely, formulas and code) in more computable form for programmatic applications. My abstract has details. I had discussions with several other attendees who would like to see this happen, although exactly how to do it needs to be worked out. [Eric Rowland]

Someone (Alois?) suggested showing even larger programs inline, collapsed by default but with some sort of "unhide" button. I suspect this is relatively easy to do with modern styling (CSS) capabilities - it's certainly supported by MediaWiki tables. [Hugo van der Sanden]

An improved Interface. Possible Directions:
a. Given an input sequence provide info about "related" sequences
b. Add mechanisms to TAG existing sequences. Allow only "meaningful" TAG types
A dream: Classification of OEIS sequences [James Abello]

Standardize names of programs based on what they do: generate the n-th term, check membership in the sequence, generate the first n terms, generate the terms up to x, print terms (discouraged!), visualize the sequence, etc [Charles Greathouse, Eric Rowland]

In the search page, have a small red X that will erase the default sequence 1,2,3,6,11,23,47,106,235,... [Eric Angelini]

Suggestions for improving the submission process

When a new sequence is submitted, the draft database is not searched. This a serious problem. [Odimar Fabeny]

I'm almost certain that in the old days, people submitting new sequences or comments were automatically thanked for their submissions. This is no longer the case, and the submissions process is, in general, significantly more frustrating and less rewarding in other ways. Can a new "thanks" message please be added? [Matthew Vandermast]

There's no automatic "thanks" message for the editors, either, as far as I know. If not, I think that would be also be a good idea. [Matthew Vandermast; edited Oct 16 2014 by Matthew Vandermast]

There is a problem on data entry in the OEIS form (special characters create a dancing system) [Odimar Fabeny]

There was a suggestion to run SuperSeeker automatically over new submissions, and mention the results in the pink box and/or email them to the submitter. [Hugo van der Sanden] Submit each proposed sequence to Superseeker (or a superseeker variant which performs fewer tests) and post results as a pink box comment if any matches are found [Charles Greathouse]

Check if a proposed sequence (1) looks like a decimal expansion and (2) lacks the keyword "cons", and if so suggest adding "cons". (Don't just add it, of course!) [Charles Greathouse]

It would be nice if admin@oeis.org would send you an email telling you when a sequence has been submitted that you might be interested in. You might specify a list of your fields of interest, or a list of A-numbers, and then anything mentioning them would trigger an email saying "You might be interested in A******. [Olivier Gerard]

A closely related suggestion: you give the OEIS a "watch list" of sequences, and when one of them gets changed, you would get an email telling you. This would be especially useful for new sequences that you have been studying. [Neil Sloane]

There should be a mechanism whereby an editor can mark a submission, saying "Leave this one to me, I will handle it". Then other editors will leave it alone. [Olivier Gerard]

We have a lot of editors, but most are not active. We need to get our editors to do more editing, on a regular basis - even if they only spend an hour or so. [Suggested by everyone]

We need to have a directory of our editors' fields of interests, so that when a sequence is submitted dealing with (say) modular forms, we can ask the appropriate editor to look at it. [Suggested by many people] I started to make such a list, but it needs to be expanded. [Neil Sloane]

As to the editing/submission form: the LINKS section should have an "autoformat" feature, similar to what is already there for the "add a supporting file" function: One would just paste the URL, and a click on a button that would "wrap" it in the HTML tags and pre-fill Author, Title, Website/Journal, Date.
Or, for known sites (mathworld, wikipedia, seqfan.eu, springerlink,...), fetch the information from the website or get it by parsing the link, or at least, by default, fill with some default text (A.U.Thor,<...>Title<...>, Journal/website, Mmm DD, YYYY). [Maximilian Hasler]

Suggestions for making the OEIS more mobile-friendly

My suggestion, mentioned at the first problem session, was to make the OEIS more mobile-friendly -- perhaps via a mobile site or an app, or some other creative solution. I do math in many venues (like while riding the train), and there isn't always a computer nearby! [Bridget Tenner]

(See William Cheswick's comment about HTML5 above)

Suggestions for improving the Sequence Fans Mailing List

In the old days there were many discussions on the mailing list about interesting sequences. In recent months this has not been the case. People should submit more postings when they see a sequence that catches their attention. [Can't remember who said this, but I certainly agree]

Suggestions for making the OEIS more appealing from a visual perspective

Dale Gerdemann recently made some very nice videos illustrating entries A001654, A010048, A005248, A002878. I added links to them. There is also an entry in the Index to the OEIS under "videos, sequences with" that list a couple of hundred such sequences. But we could use a lot more! [Neil Sloane]

The "visual" also implies some formatting, e.g. short signatures, which would reduce clutter and still provide the possibility of adding attributions even for links, references, xrefs etc..
Clutter could also be reduced via Link to discussion pages, lengthy and elaborate contributions (HTML, graphics#in comments, formulae, programs...) could be moved to the wiki.
More generally, I suggested enhanced display of sequences and/or search results and (or through) customizable user interfaces via personal preferences: colors, logo, font size, signature style, number and default format for search results, # [Maximilian Hasler],16.10.14

The graph drawing page (PLOT, PLOT2) could have an option for discarding any values larger than a selected "cut-off" value (maybe showing a specially colored dot at the value zero to indicate that the value was over the limit). This because in many sequences which are widely divergent (e.g. A122111 and many other such sequences manipulating prime indices or exponents), potentially interesting details are lost because of the "zooming out effect" with the current scatter plot. [Antti Karttunen], 27.10.2014.

Suggestions for improving the "listen" button.

The "listen" button doesn't work [Odimar Fabeny]. It doesn't work for me either. What I do is click "listen", then click "save file", then I click the saved file - and it plays right away. [Neil Sloane]

I suggested that sequences involving only products of small primes might have an alternative "listen" algorithm that would factorize the values, assign a distinct instrument to each distinct prime, and then use the exponent of each prime to determine the pitch for the instrument. [Hugo van der Sanden]

Instead of reading the sequence mod 88, read it mod 8 or 12, or 16 or 24 (to span two octaves). This would probably sound much better. [Olivier Gerard]

Add an option to map the resulting values through yet another sequence, working as a "scale", to make the results less atonal. Add an option to generate MIDI velocity values with another sequence, to get some rhythmic structure as well. [Antti Karttunen]

Suggestions concerning funding.

We discussed the possibility of using a funding model similar to the arXiv's, where institutions voluntarily contribute based on usage. There is a description here (in particular, see Sections 2.2 and 2.3): http://arxiv.org/help/support/whitepaper [Eric Rowland]

So if (say) Brown University (or Brown University Library, maybe) is a heavy user of the OEIS, we could legitimately ask them for a donation. And no doubt there are many government agencies who use the OEIS as a resource - same thing. [Neil Sloane, Oct 17 2014]

I earwigged on a discussion of funding, and mentioned some prior experiences of fundraising activities for the development of Perl, undertaken these days by The Perl Foundation (TPF, [1]), in particular that a predecessor of TPF had had a poor experience of hiring a professional fundraiser in part because nobody had the knowledge to provide appropriate oversight of the fundraiser's activities. TPF has had some success at raising money by talking directly to some of the bigger companies reliant on Perl, which sounded similar to the arxiv model of directly contacting the institutions that made the greatest use of their services. In TPF's experience, that's often best achieved by using personal relationships with individuals at those organizations to find the appropriate contacts and ease the way. But the way in which a commercial company may be reliant on Perl is very different from the way a University Maths department may be reliant on OEIS, so I don't know how mappable the experience is. [Hugo van der Sanden]

If possible, get project funding for making the OEIS more approachable to (e.g.) high-school teachers as a resource, then search for core funding with multiple pitches (education/research/etc.) [Charles Greathouse, Harvey Dale]

History of this document

This document was created by Neil Sloane (njasloane@gmail.com) on October 15, 2014, based on emails from and discussions with many people.