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Future Projects

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Future Projects

Want to Help?

The following is a list of some projects that need doing in connection with the

On-Line Encyclopedia of Integer Sequences.

If you are interested in working on any of these, please feel free to do so! My email address is All help will of course be acknowledged.   Neil Sloane.

Last updated Jun 10 2005 Comments and suggestions for additional entries are welcomed.

  • Update the references to web pages.
    In many cases the entry for a sequence just gives a link to a web page, without mentioning the author of the page, or even the title. Many simply say "Source", or "More information". Typical examples (with spaces inserted to make the line visible) are: %H A002457 < a   href= " h t t p : / / m a t h s t a t . c a r l e t o n . c a / ~ z h a o / T E A C H I N G / 7 0 . 2 6 5 / r a n d o m - v / r a n d o m - v . h t m l " >Source< / a >%H A000396 < a   href = " h t t p : / / w w w . u t m . e d u / r e s e a r c h / p r i m e s / m e r s e n n e . s h t m l " >Perfect numbers< / a >What needs to be done:Follow every link, make a note of the authors' names and the title of the page, and construct a better link and send it to me. The preferred format is:%H A060638 M. Latapy, < a   href = " h t t p : / / w w w . l i a f a . j u s s i e u . f r / ~ l a t a p y / Z o n o / i n d e x . h t m l " >Tilings of zonotopes< / a >%H A000396 J. S. McCranie, < a   href = " h t t p s : / / c s . u w a t e r l o o . c a / j o u r n a l s / J I S / V O L 3 / m c c r a n i e . h t m l " >A study of hyperperfect numbers, J. Int. Seqs. Vol. 3 (2000) #P00.1.3< / a >with the author's name first, then the title, etc., inside the link. The reasons for doing this are: to give more information about the web pages, to give more credit to the authors, and to make these web references have the same format as references to books and journals. There's no reason to distinguish between the different types of references. If a link is broken, try to find out the correct link, if necessary by contacting the author directly.
  • Many electronic journals are available on the web these days, as well as the collected papers of scientists both living and dead. See for example the web site of the European Mathematical Information Service (EMIS). Furthermore a large number of preprints in mathematics and physics are available from web sites such as the LANL eprint arXiv. What needs to be done:Scan these journals, books and preprints looking for new sequences or additional references for existing sequences. Here are some journals that very often contain integer sequences (but which I do not have time to scan):
  • Help spread the word about the OEIS
    People are constantly telling me that they just found out about the Encyclopedia, and how they wished they had known about it years ago, Many university departments, libraries, individuals, etc., publish lists of useful web sites. It would be nice if more of them would mention the On-Line Encyclopedia of Integer Sequences. What needs to be done:For any list of "useful sites" or "helpful links" that you can find on the Web, send them a message proposing that they include a link to the OEIS. Typically the following information is what they need:
    • Name: On-Line Encyclopedia of Integer Sequences
    • URL:
    • Brief description: Have you ever come across a number sequence in your work (or play)
      - such as 1, 1, 2, 3, 6, 11, 23, 47, ... -
      and wanted to find out what was known about it (or even simply the next term)? This is the place to find out.
    • Category: Mathematics (or Science) reference
    • Contact person: N. J. A. Sloane (
  • More information about asymptotics.
    What needs to be done: Go through
    • Andrew Odlyzko's survey article Asymptotic enumeration methods, pp. 1063-1229 of R. L. Graham et al., eds., Handbook of Combinatorics, 1995 (pdf);
    • also the publications of Edward A. Bender, Daniel J. Kleitman (look them up in MathSciNet), and others;
    • also any sequences that have references to "combstruct", such as A001190. (The Combstruct database often gives the asymptotic behaviour of the sequences that it mentions.) For any sequences discussed in these references, see if there is a formula known for the asymptotic behaviour of a(n) when n is large. If there is, mention this:%F A123456 For asymptotic behavior see the article by J. Smith, ...(and of course add the reference if it is not aleady present). If the formula is simple enough, then please give it:%F A123456 For large n, a(n) is asymptotic to 3*2^n - see the article by J. Smith...
  • Sequences from generalized polyominoes.
    There are a number of sequences concerned with counting polyominoes of various kinds where the description needs to be made more precise. Some examples are A056780 A056784 A056841 A056840 A056787 A056844 A056845 A056755 A056843 A056783 A056779 A056785 A056786 A056842 A056769 . What are these sequences? Many of them are taken from web pages like these: Vicher's page, Livio Zucca's page about pentominoes and this one! What needs to be done? Give a precise definition. Borrow or create a nice picture (as a gif or jpg file, say) to illustrate one of the early terms (see A000105 for an example). Track down similar sequences by following the links in these pages.
  • More illustrations for important sequences.
    Look at A000105 - note the link to a figure that illustrates one of the early terms in the sequence. I would like to get such illustrations (whenever they are appropriate) for all the important sequences, especially those with keyword "core". Sometimes illustrations can be found on the web. Often it is possible to get permission to use someone else's picture. Typically what I do is the following. Say Jane Smith has a nice web page about caterpillars.
    Add a line in the entry for that sequence in the database saying something like:
%H A123456 <a href="">Jane Smith's page about
caterpillars.</a> Make a copy of her gif or jpg file that shows the caterpillars of order 4, and link to it by a line like:  
%H A123456 <a href="a123456.gif">
Jane Smith's picture of caterpillars of order 4.</a> Of course I ask permission first. I have found that people are usually very willing to cooperate. The reason I prefer to make a copy of the gif file and put it on the sequence web site, rather than just putting in a link, is that URL's change unexpectedly. Someone said that the average life of a web site is about 6 months. The address of the sequence web site has been unchanged for at least five years. Thanks to  Henry Bottomley (se16(AT), Vladeta Jovovic (vladeta(AT)Eunet.yu),  and others who have contributed illustrations. Much more remains to be done however.
  • Look for expired links
    I have a program that I run every so often that looks to see if any of the links in the database have expired. Usually this turns up a large number of dead links. Maybe someone would be willing to look at some of the dead links, and do the detective work necessary to find out if they have moved or if they have been deleted from the Web. If the latter, people are sometimes willing to allow the OEIS to install a copy on the OEIS web site. (Perhaps the person has moved and no longer has a home page of their own.) The list of bad links as of Dec 13 2000 can be found here. What needs to be done? For each link on that list:
    • Check that it is indeed broken (I may have just been unlucky)
    • find the one or more sequences that mention it;
    • then track down what happened to it
    • send in the corrected link (or let me know if it is hopelessly lost) by filling out the [[<dont>| Comment on an existing sequence]] form.
    • The most serious thing that can happen is that the only known description of a sequence is on the missing web page. In this case it is important to try to recover the definition of the sequence! Thanks mostly to the work of James Sellers (sellersj(AT), the list of bad links is now empty. Many thanks, James!
  • More Maple or Mathematica programs for important sequences.
    Many entries have programs in Maple, Mathematica, Pari, Magma, etc. which generate the sequence. I would like to get such programs (whenever they are appropriate) for all the important sequences, especially those with keyword "core" or "nice".
  • More Engel expansions
    Take a look at A006784 . It would be nice to have Engel expansions for more of the standard constants (sqrt(2), the golden mean, etc.). I did not look to see what expansions are there now (see the Index file for this) but there are not many I believe. Jan. 17, 2001: Many thanks to Mitch Harris (maharri(AT) who has followed up on this suggestion. See the expanded list of sequences related to Engel expansions in the Index file.
  • Sequences from binomial coefficient identities.
    Look at A037967 . I would like to get lots more sequences like this. What needs to be done:Pick one of the standard references that gives lists of binomial coefficient identities. For a sum that depends on a single parameter n (such as that in A037967 ) convert it into a sequence (and give both sides of the identity). For a sum with two parameters m and n, convert it into a triangular or square array and hence into a linear sequence by reading the array by rows or by antidiagonals. See the file Welcome to the On-Line Encyclopedia of Integer Sequences for more information about converting arrays into sequences. If the values of the left- and right-hand sides are integers, then that's the sequence. If they are fractions, then as usual enter the numerators and denominators as separate sequences, with keyword "frac" and linked together by cross-references. H. W. Gould's "Combinatorial Identities" is the obvious place to start. I have added a handful of sequences from it, but have not gone through it in any systematic way. Please give references for the binomial coefficient identities that you are using. Dec. 29, 2000: Many thanks to Yong Kong (ykong(AT), who has sent in many new sequences or comments on existing sequences based on binomial coefficient identities from the book A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, "Integrals and Series", Volume 1: "Elementary Functions", Chapter 4: "Finite Sums", New York, Gordon and Breach Science Publishers, 1986-1992.
  • Sequences from inequalities.
    Look at A055682 . I would like to get lots more like this sequence (see also previous item). D. S. Mitrinovic et al.'s Handbook of Number Theory, Kluwer, is a good source for inequalities in number theory. I have extracted a handful of sequences from it but have not gone through it in any systematic way. Please give references for any inequalities that you use.
  • Sequences from discrete math or other books.
    Pick your favorite book on combinatorics, discrete math., number theory or other branch of science, and make a concordance file listing all the sequences in it, whether explicit or implicit - from the solutions to problems, for instance. See the files giving the sequences in Comtet's Advanced Combinatorics, Harary and Palmer's Graphical Enumeration and Stanley's Enumerative Combinatorics for examples of such concordances. What needs to be done: ideally, work through the book, do all the problems, and keep track of all the sequences that occur. (Remember that sequences of rationals numbers are handled by giving separate sequences for the numerators and denominators.)For each sequence found, make sure it is in the database, and [[<dont>| send it in as a new sequence]] if it isn't, with a reference to the book, of course. If the sequence is already in the database, check that there is a reference to the book from that sequence, and if there isn't, send that in as a [[<dont>| Comment on an existing sequence.]]Some books that could be treated in this way are the following. (These are books from which I have already extracted many sequences.)
    • M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings) (An electronic version of this book is being prepared - it would be nice to arrange to have links to this version.)
    • F. Bergeron et al., Combinatorial Species and Tree-Like Structures, Camb. 1998.
    • E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982
    • T. J. I'a. Bromwich, Introduction to the Theory of Infinite Series, Macmillan, 2nd. ed. 1949.
    • J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, NY, 1996
    • J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, Springer-Verlag, 3rd edition.
    • R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 2nd edition.
    • R. K. Guy, Unsolved Problems in Number Theory, second edition.
    • F. Harary, Graph Theory, Addison-Wesley, 1969.
    • G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers [since there are many editions of this book, if possible references should avoid mentioning page numbers.
    • D. E. Knuth, The Art of Computer Programming, 3+ Vols. Of course it would be too big a job to go through every page of this work looking for sequences. But even a partial concordance would be useful. Many more sequences are waiting to be extracted from these books. Since there are many different editions of each volume on people's shelves, if possible references should be written so as to refer to chapters, sections, equation numbers and paragraphs, rather than to page numbers.
    • J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958
    • J. Riordan, Combinatorial Identities, Wiley, 1968
  • Sequences from the physics literature.
    More than 20 years ago I scoured all the main physics journals (J. Math. Phys, J. Phys. A, etc etc) and found many sequences. This needs to be done again! Of course for recent papers one can also check the LANL web site.
  • Sequences from the chemistry literature.
    More than 20 years ago I scoured the chemical journals like J. Math. Chem. and found many sequences. This needs to be done again! The relatively recent journal MATCH especially needs to be checked. What needs to be done: Look at all the issues of the appropriate journals, MATCH, Combinatorial Chemistry, J. Math. Chem., etc. Also look for papers in the indexes to the chemical literature for papers with "number of" or "enumeration" in the title or abstract. Note in particular that Combinatorial Chemistry can be accessed freely if one is a subscriber to ChemDex (and that is also free). On Dec 13 2000 Elemer Labos (labos(AT) made the following suggestions:"Concerning chemical items I know of a group of German and Croatian authors who published a large amount of Computer Generated Organic Molecules ... data (isomer enumeration in the style of Cayley or Polya)."This was in the Cayley -- Polya tradition. In 1985 they published a lot of isomer enumeration data. Not only trees, rooted trees, physical trees but also condensed hex-es of the most diverse types. I am sure you could find new things in their work."A very interesting paper is Knop JV, Mueller WR, Szymanski K, Trinajstic N, Computer generation of certain classes of molecules. SKTH/Kemija u industrij, Zagreb, 1985, 210 pages"I found Nenad Trinajstic on the Internet as follows:
CROATICA CHEMICA ACTA Editor in Chief - N e n a d T r i n a j s t i c
    Editor-in-Chief of Croatica Chemica Acta since 1994 N. Trinajstic
    is a senior scientist at Rudjer Boskovic Institute, full prof. at
    Faculty of Science , University of Za

(1999) No.
    1 Croat. Chem. Acta Vol. 72 No. 1 I-II, 1-133, A1-A63, B1-B5,
    C1-C6 (1999) Zagreb, March, 1999 CONTENTS Editorial . . . Nenad
    Trinajstic I-II Physical and

"I think they would be happy to send you their 1985 publication, including a lot of graphical enumeration data."Also I found a coauthor of Trninajstic perhaps in USA ??


1. N. Bodor, E. Pop and N. Trinajstic, "Valence Shell and p Electron
SCFMO Calculation for the Isomerism of the
21-Benzylidene-20-oxo-pregnane Derivatives." Rev. Roumaine Chim., 16,
1427-1433 (1971).

2. L. Klasinc, E. Pop, N. Trinajstic and J. V. Knop, "Theoretical
Studies of Positional Isomers Obtained by Annelation of Benzene and
5-Membered Ring Heterocyclics Containing N, O or S." Tetrahedron, 28,
3465-3474 (1972).

3. L. Klasinc, N. Trinajstic and E. Pop, "Theoretical Study of
Isomeric Thienylfurans." Rev. Roumaine Chim., 18, 89-98 (1973).

4. E. Pop, N. Trinajstic and L. Klasinc, "Theoretical Studies of Some
Furocoumarine Isomers." Rev. Roumaine Chim., 18, 1249-1257 (1973).

115. E. Pop, "Water-Soluble Combinations of Dexanabinol: Prodrugs and
Analogs", Die Pharmazie, 55, 000-0000 (2000).

Contact information:

Alchem Laboratories Corp        Tel: (904)418-1650       FAX:  (904)418-1584
13305 Rachael Boulevard, Alachua, Florida 32615 U.S.A., info(AT)

"I think this Dr Pop can give information on how to contcat Trinajstic and get (I am sure in) intersting raw material for EIS."Their polyhex isomers seem to me 2D dominoes or animals ."The German coauthor J. V. Knop was 15 years ago in University of Duesseldorf , Computer Center. I could not find him through the Internet.[End of quotation]

  • Mysterious or badly-described sequences
    If a sequence has the with keyword "obsc", for "obscure", it means I was unable to understand the description.
    The keyword "uned", for "unedited", means that I did not have the time to edit the entry in the usual way, which is to:
    • check that the description is mathematically sensible
    • check that all the lines are in correct English
    • check that all the lines have the appropriate labels - any Maple lines begin %p, any Mathematica lines begin %t, etc. All such sequences need to be cleaned up. What needs to be done: for any sequence that has keyword "uned" or "obsc", try to understand the description of the sequence, rewrite the description more clearly and in correct English, and polish up all the other lines in that entry.
  • Editorial assistance
    Quite often I get correspondence about sequences that calls for a fair amount of thought to understand. For example, complicated messages discussing whether two sequences are really the same. It is great fun working through such material, but I'm willing to share the fun, if there are volunteers.
  • This sequence (and any others from the same source) needs a better reference (and a better description if possible):
%I A037294
%S A037294 2,7,18,42,90,186
%N A037294 Number of (s,2) gates.
%D A037294 E Detjens and G Gannot, Technology mapping in MIS, pp. 116-119 of some 1987 IEEE conference proceedings [ # CH2469-5/87 ].
%K A037294 nonn
%O A037294 1,1
%A A037294 N. J. A. Sloane (
  • Improve the index.
    The index to the database needs a lot of work. What needs to be done: pick a topic that interests you and make an index to all the sequences that deal with that topic. For an example, look at the entries under Trees in the index. Thanks to Christian G. Bower (bowerc(AT), Mitch Harris (maharri(AT), Wolfdieter Lang (wolfdieter.lang(AT), and others who have contributed sections to the index. Much more remains to be done howeever.
  • Inadequate references
    In a number of cases the references for a sequence just give a volume and page number but not the author or title, etc. (for a typical example see A033874 - there are lots more like this). In other cases there are references saying things like "[Ii]n [Pp]reparation", "[Pp]reprint", "[Mm]anuscript", "[Ss]ubmitted", "[Tt]o [Aa]ppear", "[Ii]n [Pp]ress", etc. What needs to be done:Update all the incomplete or out-of-date references. Ideally every reference should give full details. Here is the preferred format:
    • A. B. Smith, Title of paper, Name of Journal, Vol. 66 (2000), 34-45.
    • J. H. Smith, Problem 56, Name of Journal, Vol. 66 (2000), 34-45.
    • M. K. Smith, Title of Book, Publisher, Place, Edition, Year; see especially Eq. (100) on page 564.
  • Update the French version
    The French version is quite out of date. Originally it was a direct translation of the English version. But since then I have completely changed the English version several times. What needs to be done is to translate the English versions of the current pages into French, and completely redo the French version, making it parallel to the English version.
  • More terms.
    There is a long list of sequences that need extending.
  • Links to MathSciNet
    I wish it were possible to have a link to MathSciNet whenever the entry for a sequence cites a paper or book that has been reviewed by Math. Reviews. However, since MathSciNet is a commercial service - and so not accessible to the general public - I don't see hope of doing this at present. Hopefully one day it will be freely available.
  • General remarks
    • Note that if you are contemplating doing serious work on the database, it is possible to download any section of it by going to the file Welcome to the On-Line Encyclopedia
    • If you have occasion to write to someone while working on one of these projects, feel free to say something like "I'm helping Neil Sloane with the On-Line Database of Integer Sequences and the following question has arisen in connection with your sequence A****** ..."
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