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Need help with sequences from enumeration of curves etc. (Neil Sloane, October 2019)

I just created sequences A328550-A328555.  This is just the tip of an iceberg.

It would be worth searching the references listed in the sources for those sequences (and the references in those references, etc.), looking for other sequences not in the OEIS.

Search The Ramanujan Journal for sequences (Neil Sloane, October 2019)

I never see this journal, but I stumbled across it by accident recently. It seems to have a lot of sequences buried in the articles. (You really have to look inside the articles, because you can't always tell from the titles.)

It doesn't have many references to the OEIS - this is a journal from a different world. There are 50 volumes, maybe 150 issues. Springer has it behind a pay-wall.

I have added a bunch of sequences from a few random issues that I looked at - see A328527 onwards.

I didn't have time to enter all the sequences from this article:

Köklüce, Bülent. "Cusp forms in S_6 (Gamma_ 0(23)), S_8 (Gamma_0 (23)) and the number of representations of numbers by some quadratic forms in 12 and 16 variables." The Ramanujan Journal 34.2 (2014): 187-208. See p. 196. (A028930 is Phi_1, A028959 is F_1.)

In particular, the nine sequences with

G.f. = Phi^i*F^j, (i+j=8) where Phi = g.f. for A028930, F = g.f. for A028959. on page 204 could be added (compare A328536).

Look through the Gathering For Gardner Gift Books for sequences (July 2019)

Check these books for new sequences (and add them to the OEIS), or existing sequences (adda link from the OEIS entry to the book).

G4G10 Papers:

G4G11 Papers:

G4G12 Papers:

G4G13 Papers:

The G4G10, G4G11, G4G12, and G4G13 exchange papers are all available for free.

"The complete PDF of the G4G13 exchange book (with cover art and table of co=ntents) will also be available online soon."

N. J. A. Sloane 12:53, 22 July 2019 (EDT)

Small or one-time sequence projects

  1. {{Sequence of the Day for March 1 2014}} through {{Sequence of the Day for March 30 2014}}. Choosing sequences and writing up a sentence or two about one interesting aspect of those sequences.
    Done for Mar 29 - Mar 31. Many among Mar 01 - Mar 28 still missing. MFH 23:11, 9 March 2014 (UTC)
  2. I or s/o else should do the same edit done in for A210414, A210416-A210423:
    1. Add < a href="/index/Se#self-referencing_sequences" >Index to the OEIS: Entries related to self-referencing sequences< /a >.
    2. Change the NAME in the same way.
    3. Add %Y Cf. A098645, A098670, A114134. (or not!? and/or add most relevant XREFS from the index?)
      Thanks in advance! — M. F. Hasler 15:47, 10 October 2013 (UTC)
  3. Replace "" by "/wiki/Catalog_of_Toothpick_and_CA_Sequences_in_OEIS". Thanks in advance! - Omar E. Pol 14:26, 9 January 2014 (UTC)
    This appears to have been done. As a follow-up, can we delete Toothpick_sequences and leave Toothpick_problem. Then Category:Toothpick_structures can be moved out of Category:Toothpick_sequences and placed directly in Category:Toothpick_problem. - Danny Rorabaugh 15:12, 25 September 2015 (UTC).
    I disagree with Danny's proposals. I think that only Category:Toothpick_problem should be deleted. Omar E. Pol 22:55, 24 October 2015 (UTC)
    I'm fine with keeping either one: there's just unnecessary Inception going on the way it is now. - Danny Rorabaugh 03:15, 25 October 2015 (UTC)
  4. Replace "shell model of partitions" by "modular table of partitions". (~ 86 sequences). Thanks in advance! - Omar E. Pol 12:50, 11 March 2014, 25 October 2015 (UTC)
  5. On Sat, Nov 1, 2014 at 3:03 PM, JM Bergot <> wrote: I just now looked at suggestions & other stuff from the get-together in early Oct. I couldn't see how to make a suggestion, not as if OEIS needs more of them. If I am certain that 5578, 12777 or 23,457,1223 are the first terms of a sequence and can find NO other with simple implements, shouldn't there be a way of getting ALL seqs beginning with these two or three numbers rather than listing ALL sequences containing them? This would mean not having to go through mounds of sequences where these numbers occur any place.
    This would be especially useful when searching for constants. You might know only a few terms, giving 300 matches, but only 10 of which match starting from the beginning. - Charles R Greathouse IV 15:03, 18 December 2014 (UTC)
  6. Add a link from the Draft page of every user to the page . Thanks in advance! - Omar E. Pol 18:14, 12 December 2014 (UTC)
  7. It would be nice to have the total number of entries in the pages of, for example, "Total number of entries: 256" below of the title "Proposed drafts" or above of "Showing entries 1-100 | older changes". The same for the pages of Omar E. Pol 13:14, 11 October 2015 (UTC)
  8. Change links like "" to "". That is, "" needs to be replaced with "", and "" prefix needs to be removed. - Max Alekseyev 04:58, 29 November 2017 (UTC)

Large or ongoing sequence projects

  1. Look through journals and books, especially those available on the web, for (a) new sequences (add them!), (b) references to existing sequences (add a reference or link to that entry), and (c) mentions of the OEIS (add them to the list of "Works Citing the OEIS" on the wiki). The following is a partial list of journals and books to look at.
    Electronic J. Combinatorics
    Directory of open access journals (clicking on "Browse" on the left then on "Mathematics and Statistics" leads to the mathematical branch)
    Electronic Research Announcements of Amer. Math. Soc.
    European J. Combinatorics
    Experimental Mathematics
    Fibonacci Quarterly
    Integers: Electronic Journal of Combinatorial Number Theory
    J. Chem. Inform. Comput. Sci. (Enumerative chemistry, now renamed as J. Chem. Info. and Modeling)
    J. Integer Sequences
    Nieuw Archief voor Wiskunde
    Royal Society journals
    Wikipedia list of math journals
    Small collection of links
  2. Max Alekseyev, automated discovery of unknown formulae, posting to SeqFan on Oct 25 2011. The project is ongoing at the George Washington University. — Max Alekseyev 12:57, 25 December 2011 (UTC)
  3. Indexing/cross-referencing large [and especially poorly documented/cross-linked] "series", e.g. Decimal expansion of 1/3, 2/3, 1/6, 5/6, 7/6,1/7,......,1/998, (and ultimately all "cons" sequences). — M. F. Hasler 21:48, 24 October 2011 (UTC)
    BTW, this project would merit a page on its own to synchronize / show progress / manage "TO DO's", etc. — M. F. Hasler 21:48, 24 October 2011 (UTC)
  4. Improve the index (since we do not yet have categories), especially
    • for sequences of some 1000+ categories like decimal expansion of ...
    • by wikifying cross references inside the index (e.g. on the above page, "see square roots" or "decagon is spelled 10-gon..." etc.) — M. F. Hasler 03:55, 26 October 2011 (UTC)
    • Perhaps add an index to the hypergeometric recurrences in the spirit of the linear recurrences. Essentially covering all the sequences with a square root in the o.g.f. including many walks, Catalan and Motzkin sequences. — R. J. Mathar 11:46, 14 November 2011 (UTC)
      • Richard, I think this would be a great project, certainly of importance. I'm not sure what the best way to categorize them is (an analogue, hopefully, of your "signature" for linear recurrences) but I've also seen the need. Charles R Greathouse IV 04:26, 31 January 2012 (UTC)
      • Started a section in the "Rea" section of the index under "recurrences, hypergeometric" which uses a major order following the number of terms involved, a minor order following the order of the polynomial of the coeffs., and the integer coeffs. of the polys. from high to low degree. The defining convention is actually that the terms are written poly0*a(n)+poly1*a(n-1)+...=0, because the n-depend. of the poly(i) depend on the agreement on the indexing (increasing, decreasing, offset) of the a(i). Is this the most common formulation of the recurrence? R. J. Mathar 12:41, 29 February 2012 (UTC)
  5. Check terms, add proper names, edit the 1730 unedited sequences.
    The top contributors of uned sequences are Bagula at 74%, Lagneau at 3%, and Shevelev at 2%.
  6. Go through Guy's Unsolved Problems in Number Theory (UPNT) and add references (to papers referenced by Guy as well as to UPNT itself, with the section), formulas, and any other relevant material; also add new sequences as needed. I think the best approach would be a distributed project where many people each volunteer to take one or more sections. Charles R Greathouse IV 04:43, 15 March 2012 (UTC)
  7. More important and more urgent: find out the present state of Richard Guy's updates in preparation of the new edition of UPNT! - N. J. A. Sloane, Mar 20, 2013
  8. Create a "community portal" with a corner (or simply a separate page) "TO DO on OEIS", where one could post "request of jobs to be done" (instead of posting to SeqFan list), like: Errors to correct -- Please double-check, I suspect an error in Seq. Annn -- Someone who feels competent, please calculate more terms for Annn concerned with ... [I know, KW "more" essentially means the same...] -- etc. — M. F. Hasler 13:44, 24 August 2012 (UTC)
  9. Create an iOS interface or app; I'm willing to make an OEIS interface for iPhone/iPod touch/iPad. If appropriate, any suggestions on how to access the database from outside? — Jens Bossaert 18:47, 7 April 2013 (UTC)
    I'm curious as to what you'd want the application to do (beyond what the site does, of course). The project sounds interesting and I might be able to help (though I don't have an Apple developer account).
    As for accessing the database, I just use Or do you mean something else?
    Charles R Greathouse IV 18:58, 7 April 2013 (UTC)
  10. Preserve line breaks in pink-box comments. - Joerg Arndt 12:27, 25 April 2013 (UTC)
  11. Add the keyword "more" where obviously needed. I did that for up to A001500. The file stripped.gz is of great help with this task. — Joerg Arndt 13:56, 21 May 2013 (UTC)
  12. Go through sequences marked keyword:more keyword:easy and either expand or reclassify. - Charles R Greathouse IV 05:44, 19 June 2013 (UTC)
  13. Add links to those references with arXiv identifiers to make them easier to follow. The search responds with 9 pages (approx. 90 sequences) as of 04 May 2017.
  14. Conservation of web pages linked to from OEIS, from Neil Sloane, Oct 08, 2013
  15. It would be nice to have a third Plot in the button “Graph”. The appearance of the third Plot should be the same as "Plot 2" or “Plot pairs of sequences in the OEIS” with the following configuration: Sequence 1: A?????? untransformed (our sequence). Sequence 2: A000004 (always) untransformed. Contents of Plot: “Plot Seq2(n+shift) vs n and Seq1(n) vs n”. Appearance of Plot: “Draw line segments” (only). For instance, see this proposed Plot for A005132 Recaman’s sequence. See also this proposed Plot for A064413 EKG sequence. I think that a large number of sequences may show a nice graph using this proposed Plot. Omar E. Pol 15:20, 30 November 2013 (UTC)
  16. Add the index to the signature of the linear recurrences and the g.f. to each of the sequences A037674 - A037799. - R. J. Mathar 19:16, 30 April 2015 (UTC)
  17. Allow editors to sort the "Sequences awaiting review" by other columns. - Danny Rorabaugh 14:38, 25 September 2015 (UTC)
  18. Is it possible for a search for "Lukasiewicz" to give both "Lukasiewicz" and "Łukasiewicz" and for "Waclaw" to give both "Waclaw" and "Wacław"?. - Danny Rorabaugh 16:53, 13 October 2015 (UTC)
  19. What would be the best way to index, collect, or highlight the open questions, conjectures, and empirical observations on OEIS? I would love to have a keyword "conj" and/or a new section OPEN PROBLEMS within the entries so problems that are still open can be more easily identified. The keyword could be used for entries with questions specifically related to the sequence, not just for sequences related to some conjecture. The section could contain only the still unanswered items, with any questions that are subsequently answered moved to COMMENTS. - Danny Rorabaugh 18:59, 12 May 2016 (UTC)
    It is an interesting idea, and it has been considered in the past. The trouble is, almost every entry - well, say fifty thousand entries - would end up with that keyword. If you search in the OEIS for the phrases "empirical", "conjecture", "appears that", "would be nice to", "wanted", and other synonyms, you will see what I mean. And that just accounts for sequences where the contributor knew enough to admit that there was no proof. I have found that when I ask someone if they have a proof for a formula they have added to a sequence, 90% of the time the reply is "No, it just seemed to be true but I don't have a proof". So, unfortunately, formulas or comments that have been proved are in the minority. Of course such formulas are still extremely valuable to anyone who came across the sequence and wanted to know more about it. - N. J. A. Sloane 01:24, 13 May 2016 (UTC)
    Of the ~50k, I sense that a substantial proportion are sequences related to conjectures or are statements that have already been (dis)proved. And yes, I see assumed formulas as a recurring issue. I think having an explicit place for unproved ideas would help sort through those, and make them more available to fledgling mathematicians. - Danny Rorabaugh 04:08, 13 May 2016 (UTC)
    I think it would be nice to have a list of these, but I expect there are many thousands of them. Maybe put it on the wiki? - Charles R Greathouse IV 20:06, 13 May 2016 (UTC)

Requested sequences

If you have an idea for a new sequence and would like help with computing terms, straightening out the definition etc. simply post a request below. Try to include enough information so that it's clear what sequence you have in mind. Please make your request in the form
# Your request for a sequence to be added to the OEIS ~~~~
Thank you. Felix Fröhlich 20:34, 24 August 2014 (UTC)

  1. Algebra that pertains to this function I will explain here. I used a program called Geogebra to build a function that starts with a line of 5 units from origin vertical on the y axis. the units were as small as i could get, to the -13 power(the function gets large to the 13th power quickly). I used the regular polygon tool to make n+ polygons counterclockwise, starting from origin as the first point and the third point, counterclockwise, in the polygon prior, as the base for the next n+ polygon. as the polygons become larger zooming out is required and eventually comes to the point that the program won't zoom out anymore. Scrolling to the next point takes awhile using the keyboard on the computer (there is a point list on the left that allows clicking the origin point first and then clicking a point to make a base, so only getting to the next point is necessary on the screen). I started looking for patterns in the numbers of two properties. First is when the base crosses an axis/90degrees. Second is when a base changes direction off of a virtual origin and changes direction going to the next point(richochets). What I mean is when the line of the polygon created travels towards a flat plane and rebounds off it, first side and second side (counterclockwise). I obtained some numbers for crossing axis directions, being 5,8,12,20,32,52,84, the first number being crossing the vertical axis +y/180degrees. The second set was [3?4?],6,8,15,30,50,82. The first number being confusing but probably 3. The sequences for the rebounds seem to always be before the turns over the axis and also do not share as apparent similarity to those numbers as well. The numbers are the numbers of points/sides to the polygon. I am wondering if there are functions to explain the spirals formed in this function and what they are. I was originally looking for other spirals than the golden spiral. — Ryan Lawrence Austin 00:46, 19 February 2015 (UTC)
  2. Wall-Sun-Sun primes or Fibonacci-Wieferich primes (Wall-Sun-Sun prime, Wikipedia). Felix Fröhlich 20:34, 24 August 2014 (UTC)
  3. Meertens numbers (Meertens number, Wikipedia), Cf. A246532. Felix Fröhlich 20:34, 24 August 2014 (UTC)
    1. Max Alekseyev and David Applegate pushed this search to 10^45 without finding another term (Re: Meertens numbers, Seqfan). Felix Fröhlich 12:17, 19 February 2015 (UTC)
  4. Composite numbers satisfying the same definition as 3737 given in paper (Romeo Mestrovic, A congruence modulo n^3 involving two consecutive sums of powers and its applications, arXiv, see page 8). The only known term is 3737 and there are no others up to 16000. Felix Fröhlich 20:34, 24 August 2014 (UTC)
  5. Lucas-Wieferich primes (R. J. McIntosh, E. L. Roettger, A search for Fibonacci-Wieferich and Wolstenholme primes, Math. Comp. Vol. 76, No. 260 see page 2088). Felix Fröhlich 20:44, 24 August 2014 (UTC)
  6. Wieferich primes to base 11. Only one such prime is known (71) and any other one must be larger than approximately 5.9*10^13 (see R. Fischer, Thema: Fermatquotient B^(P-1) == 1 (mod P^2)). If a second such prime could be found, A178871 could be extended as well. Felix Fröhlich 21:21, 29 August 2014 (UTC)
  7. Number of Johnson polytopes by dimension for dimension n > 2, i.e. convex polytopes whose facets are n-1 dimensional convex regular polytopes but which are not regular or uniform. Felix Fröhlich 08:29, 13 September 2014 (UTC)
  8. Number of convex deltatopes by dimension for dimension n > 2, i.e. convex polytopes whose facets are n-1 simplices. Felix Fröhlich 08:29, 13 September 2014 (UTC)
  9. Number of space-filling n-hedra for n > 5 (Space-filling Polyhedron, MathWorld). Felix Fröhlich 09:07, 13 September 2014 (UTC)
  10. Number of space-filling convex polytopes with regular facets by dimension for dimension n > 2 (Space-filling Polyhedron, MathWorld). Felix Fröhlich 12:57, 13 September 2014 (UTC)
  11. Decimal expansion / initial digits of Graham's number. Felix Fröhlich 14:06, 14 September 2014 (UTC)
  12. Descartes numbers. The only such number currently known is 198585576189 (Descartes number, Wikipedia). Felix Fröhlich 19:49, 22 October 2014 (UTC)
    (See Descartes number, also called an "odd spoof perfect number", on OEISWiki.) — Daniel Forgues 05:00, 19 June 2015 (UTC)
  13. Quasiperfect numbers (Quasiperfect number, Wikipedia). Felix Fröhlich 19:49, 22 October 2014 (UTC)
  14. Numbers n such that 10^999999+n is a megaprime. Felix Fröhlich 22:51, 29 October 2014 (UTC)
    1. We need a minimum of 3 terms for a sequence, and as far as I know we only have one: 593499, corresponding to a Frobenius probable-prime. As much as I like this sequence (having kicked off the process, in a way, though I was not involved with the computation) it's not yet ready. ~10^5 more probable-prime tests would be needed to discover the next two terms, taking many CPU-years. - Charles R Greathouse IV 05:45, 30 October 2014 (UTC)
      1. Yes, the sequence is definitely not ready to be added yet and it might be several years (or more?), but that's okay at least for me. My intention for this section is for sequences which one possibly can't compute enough terms within a few hours/days/weeks... and which are assumed to be too hard to be added anytime soon, but for which enough terms might eventually be found to be added in the future. I also regard it as kind of a challenge proposed to everyone interested to find additional terms of the sequences listed here or to develop new algorithms to find them. The long-term goal is of course to have them all added to the OEIS eventually. Felix Fröhlich 21:39, 30 October 2014 (UTC)
  15. Baillie-Pomerance-Selfridge-Wagstaff pseudoprimes (i.e. composites where PARI's ispseudoprime function (with flag 0) returns 'true', see Baillie–PSW primality test, Wikipedia). According to Arithmetic functions, PARI/GP Home, if such a number exists, it must be larger than 2^64. Felix Fröhlich 22:48, 4 November 2014 (UTC)
  16. Primes p such that (p, p - 5) is an irregular pair. The only known instance of such a prime is 37 (see this paper, page 114). Felix Fröhlich 22:26, 18 March 2015 (UTC)
  17. Primes p such that (p, p - 7) is an irregular pair. There is no known instance of such a prime (see this paper, pages 114-115). Felix Fröhlich 22:26, 18 March 2015 (UTC)
  18. Superabundant numbers (A004394) that are not Harshad numbers (A005349). The only known term is 149602080797769600 (see Superabundant number, Wikipedia and the comment by T. D. Noe in A128702 from 2009-10-27). Felix Fröhlich 22:35, 18 March 2015 (UTC)
  19. Tribonacci-Wieferich primes. There is no known instance of such a prime (see J. Klaska, On Tribonacci-Wieferich primes, The Fibonacci Quarterly, Vol. 46/47, No. 4 (2008/2009), 290-297). Felix Fröhlich 19:33, 24 March 2015 (UTC)
  20. Tribonacci-Wieferich primes of the second kind. There is no known instance of such a prime (see J. Klaska, A search for Tribonacci-Wieferich primes, Acta Mathematica Universitatis Ostraviensis, Vol. 16, No. 1 (2008), 15-20). Felix Fröhlich 19:33, 24 March 2015 (UTC)
  21. Primes p with B_{p-2}(1/3) == 0 (mod p), where B_n(x) denotes the Bernoulli polynomial of degree n. The only known term is 205129. Originally suggested as A252055. Felix Fröhlich 21:58, 13 April 2015 (UTC)
  22. Numbers that are not Hansen numbers. The only known example is 5784689 (see N. M. Clift, Calculating optimal addition chains, Computing, Vol. 91, No. 3 (2011), 265-284). Felix Fröhlich 20:14, 10 May 2015 (UTC)
  23. Minimal number of translation classes in which copies of a tile with Heesch number n can occur if as large a patch of tiles as possible is built from those copies (see Heesch numbers, Seqfan). Felix Fröhlich 14:34, 16 May 2015 (UTC)
  24. Number of n-dimensional convex uniform polytopes, excluding infinite sets. a(3) = 18, a(4) = 58. The value for a(4) was obtained by counting the distinct convex uniform 4-polytopes in Wikipedia, Uniform 4-polytope Felix Fröhlich 15:00, 16 May 2015 (UTC) [Value for a(4) updated. Felix Fröhlich (talk) 05:53, 3 October 2018 (EDT)]
    1. The value for a(3) can perhaps be derived from the set apparently proved in J. Skilling, The complete set of uniform polyhedra, Philosophical Transactions of the Royal Society A, Vol. 278, No. 1278 (1975). Felix Fröhlich (talk) 05:22, 3 October 2018 (EDT)
  25. Minimal number of pieces into which a regular n-gon must be cut such that the pieces can be rearranged into a regular (n+1)-gon, starting at n = 3. The Wallace–Bolyai–Gerwien theorem ensures this is possible for any n >= 3 (see Wallace–Bolyai–Gerwien theorem, Wikipedia). Felix Fröhlich 15:17, 16 May 2015 (UTC)
  26. Natural numbers n with n "feasible" partition(s). Only known terms are 1 and 72. Originally suggested as A254434. Felix Fröhlich 12:24, 19 May 2015 (UTC)
  27. Kissing number of Platonic solids (in the order tetrahedron, cube, octahedron, dodecahedron, icosahedron). a(1) = 20, a(2) = 26, a(3) = ?, a(4) = 12, a(5) = ?. To a(1): Start with a single tetrahedron. Attach a tetrahedron to each face of the first tetrahedron (this gives 4 "kissing" tetrahedra). Then, from the dihedral angle of the tetrahedron (~ 70.53°) it is clear two more tetrahedra can be added to each edge of the original tetrahedron, so 6*2 = 12 additional "kissing" tetrahedra. Finally, one further tetrahedron can be added to each vertex of the original tetrahedron, which gives 4*1 = 4 additional tetrahedra. Thus alltogether there are 4 + 12 + 4 = 20 kissing tetrahedra. Felix Fröhlich 12:47, 19 May 2015 (UTC)
    1. The value of a(3) is perhaps given in D. G. Larman and C. Zong, On the Kissing Numbers of Some Special Convex Bodies, Discrete & Computational Geometry, Vol. 21, No. 2 (1999), 233-242. Can someone who has access to the paper check? Felix Fröhlich 13:09, 15 May 2016 (UTC)
      1. The authors of the paper give the translative kissing number and the lattice kissing number of the octahedron, both of which are equal to 18. However, this value may not be the maximal Kissing number possible for the octahedron, as there may be a higher kissing number that is not translative or a lattice kissing number, if I understand the matter correctly. Felix Fröhlich (talk) 03:45, 7 March 2018 (EST)
  28. a(n) = number of non-selfintersecting polydodecahedra with n cells such that any two such polydodecahedra remain invariant under rotations and/or reflections. The sequence (with offset 1) starts: 1, 1, 3 Felix Fröhlich 14:03, 19 May 2015 (UTC)
  29. a(n) = number of non-selfintersecting polyicosahedra with n cells such that any two such polyicosahedra remain invariant under rotations and/or reflections. Felix Fröhlich 14:17, 19 May 2015 (UTC)
  30. a(n) = number of different room numberings such that the 'Cube' from the film 'Cube' is working (the rooms are assumed to be moving simultaneously for this sequence and how they move is irrelevant, so, only the positions before or after the move matter) and has exactly n trapped rooms. The cube consists of 26^3 rooms. A room is considered to be trapped if at least one of the three numbers is in A000961, (i.e. A001221(n) = 1). The rules for room movement are as specified in 'Burkard Polster, Marty Ross, Math Goes to the Movies, pp. 92-95 (ISBN 978-1-4214-0483-7 / 978-1-4214-0484-4)'. Obviously, the sequence is finite, with 17577 terms (with offset 0). Felix Fröhlich 14:49, 19 May 2015 (UTC)
  31. Triangle T(n, k) of members of smallest Wieferich n-cycle. A Wieferich n-cycle here is defined as an ordered set of primes p_1, p_2, ... p_i, where each prime is the smallest Wieferich prime in base equal to its predecessor. The triangle starts
    2, 1093
    3, 11, 71
    The following PARI-program can compute the triangle:
    smallestwieftobase(n) = forprime(p=2, , if(Mod(n, p^2)^(p-1)==1, return(p)))
    wiefcyclelengthof(n) = i=1; b=smallestwieftobase(n); while(b!=n, b=smallestwieftobase(b); i++); return(i)
    for(n=2, 10, forprime(q=2, , if(wiefcyclelengthof(q)==n, print1(q, ", "); j=n-1; while(j > 0, q=smallestwieftobase(q); print1(q, ", "); j--); print(""); break({1}))))
    Felix Fröhlich 20:14, 19 May 2015 (UTC)
  32. Minimum number of tiles in an aperiodic set of Wang hypercubes in dimension n (see Wang tile, Wikipedia for an overview). Felix Fröhlich 20:58, 19 May 2015 (UTC)
    1. It seems now to be proven that a(2) = 11 (see E. Jeandel and M. Rao, An aperiodic set of 11 Wang tiles, arXiv:1506.06492). Felix Fröhlich (talk) 08:46, 1 March 2018 (EST)
  33. Numbers n such that A000292(n) is a square. Only known terms are 0, 1, 2 and 48. Originally suggested as A256002. Zak Seidov searched to 10^10 without finding another term. Felix Fröhlich 21:07, 16 June 2015 (UTC)
  34. Number of uniform honeycombs in n-dimensional hyperbolic space (Uniform honeycombs in hyperbolic space, Wikipedia). Felix Fröhlich 09:02, 7 August 2015 (UTC)
  35. Minimal number of colors needed in a set W consisting of n Wang tiles such that W is aperiodic (see Wang tile, Wikipedia for an overview). Felix Fröhlich 09:06, 7 August 2015 (UTC)
    1. It seems now to be proven that a(11) = 4 and that a(n) does not exist for n < 11 (see E. Jeandel and M. Rao, An aperiodic set of 11 Wang tiles, arXiv:1506.06492). Felix Fröhlich (talk) 08:46, 1 March 2018 (EST)
  36. Number of ways of placing n nonattacking rooks on a hexagonal board with edge-length n in Glinskis hexagonal chess (see Gliński's hexagonal chess, Wikipedia). Felix Fröhlich 13:39, 18 October 2015 (UTC)
  37. Number of ways of placing n nonattacking bishops on a hexagonal board with edge-length n in Glinskis hexagonal chess (see Gliński's hexagonal chess, Wikipedia). Felix Fröhlich 13:39, 18 October 2015 (UTC)
  38. Number of ways of placing n nonattacking queens on a hexagonal board with edge-length n in Glinskis hexagonal chess (see Gliński's hexagonal chess, Wikipedia). Felix Fröhlich 13:39, 18 October 2015 (UTC)
  39. Number of ways of placing n nonattacking knights on a hexagonal board with edge-length n in Glinskis hexagonal chess (see Gliński's hexagonal chess, Wikipedia). Felix Fröhlich 13:39, 18 October 2015 (UTC)
  40. Number of ways of placing n nonattacking kings on a hexagonal board with edge-length n in Glinskis hexagonal chess (see Gliński's hexagonal chess, Wikipedia). Felix Fröhlich 13:39, 18 October 2015 (UTC)
  41. Triangle T(n, k) of number of spheres of radius k for k = 1, 2, 3, ..., n that can simultaneously touch a central sphere of radius n, read by rows. Felix Fröhlich 16:25, 8 January 2016 (UTC)
  42. Minimal number of additional convex tiles required such that the n-th Platonic polyhedron can tile Euclidean 3-space, in the order tetrahedron, cube, octahedron, dodecahedron, icosahedron. a(1) = 1, because the tetrahedron tessellates space with the octahedron in the tetrahedral-octahedral honeycomb, a(2) = 0, because the cube is a space-filling polyhedron, a(3) = 1, because of tetrahedral-octahedral honeycomb, a(4) = ?, a(5) = ?. Felix Fröhlich 16:30, 8 January 2016 (UTC)
  43. Number of regular compounds of regular polytopes in n dimensions. Originally suggested as A266814. Felix Fröhlich 10:50, 10 January 2016 (UTC)
  44. Number of hermitian indecomposable unimodular lattices over the ring of Eisenstein integers of dimension n. Apparently, a(8) = 720 (cf. (C), table 1), a(9) = 648 (cf. (C), table 1), a(10) = 540 (cf. (C), table 1), a(11) = 396 (cf. (C), table 1), a(13) = 14 (cf. (B)), a(14) = 58 (cf. (A), theorem 1), a(15) = 259 (cf. (A), theorem 2) (A) (B) (C). Felix Fröhlich 11:31, 13 February 2016 (UTC)
    1. I might have misread something. According to Gitter und Anwendungen, Report No. 1/2005, Mathematisches Forschungsinstitut Oberwolfach, K. Abdukhalikov, Unimodular Hermitian lattices, p. 27-30, a(1) = a(6) = a(8) = a(9) = 1, a(10) = a(11) = 2, a(12) = 11, a(13) = 14, a(14) = 58, a(15) = 259. Some of the missing values might be given in reference [7] listed in that paper. Felix Fröhlich 15:54, 21 May 2016 (UTC)
  45. Primes that are not good. The only known term less than 10^8 is 23 (see D. M. Davis, For which p-adic integers x can sum_{k}binomial(x, k)^-1 be defined?, p. 2). Felix Fröhlich 20:55, 17 May 2016 (UTC)
  46. omega(2^(2^p-1)-1) for p = A000043(n), i.e., a(n) = A001221(A000225(A000668(n))). a(1)-a(4) are 1, 1, 1, 1. a(5) is at least 2 according to Found factors, Double Mersennes Prime Search. Felix Fröhlich 14:51, 3 June 2016 (UTC)
  47. Numbers n such that 2^n-1 is a semiprime and at least one of the two prime factors p and q satisfies p^2 =/= 1 (mod n) or q^2 =/= 1 (mod n) (see this question at Mathematics Stack Exchange). Greg Martin at MSE states he searched to n = 200 and found only two cases: 9 and 49. I extended the search to 292 without finding another term using the following PARI code: is(n) = my(t=2^n-1); if(bigomega(t)==2, my(p=factor(t)[1, 1], q=factor(t)[omega(t), 1]); if(Mod(p^2, n)==1 && Mod(q^2, n)==1, return(0), return(1))). Felix Fröhlich 13:24, 21 June 2016 (UTC)
  48. Integers z such that x^3 + y^5 = z^7 has a solution for x, y, z > 0. Known terms are 8192 and 268435456. Originally suggested as A273913. Felix Fröhlich 20:58, 6 July 2016 (UTC)
  49. Elliptic Carmichael numbers. The smallest term is 617730918224831720922772642603971311. See arXiv:1609.00231. Felix Fröhlich 11:17, 13 August 2017 (UTC)

Done requests

If any of the above requested sequences have been created, please move the entry of the request (including any discussion) to this section and provide a link to the created sequence entry in the database. Felix Fröhlich 20:35, 20 May 2015 (UTC)

  1. A249275: Smallest a such that prime p satisfies a^(p-1) == 1 (mod p^3) ([1] see page 929) Felix Fröhlich 07:26, 14 September 2014 (UTC)
  2. A275338: Smallest prime p such that some base b with 1 < b < p exists for which p satisfies b^(p-1) == 1 (mod p^n), i.e., smallest p = prime(i) such that A254444(i) == n. Sequence (with offset 2) starts 11, 113 Felix Fröhlich 14:17, 19 May 2015 (UTC)
  3. A275773: Counterexamples mentioned in comment from Bruno Berselli in A059245: Primes congruent to 1 modulo 13 such that x^13 = 2 has a solution modulo p. a(1) = 4421. Felix Fröhlich 15:54, 8 January 2016 (UTC)
  4. A283449: Smallest composite that is not an n-th power, but can be written as the sum of the n-th powers of two or more of its prime factors. a(7) = 275223438741 (cf. A257659). Felix Fröhlich 15:45, 8 January 2016 (UTC)
  5. A309442: The analogue of A244951 in four dimensions, i.e., the minimum number of colors needed to color the cells (facets) of the six Platonic 4-polytopes such that no two cells meeting at a common "ridge" share the same color. Felix Fröhlich 14:03, 19 May 2015 (UTC)


  1. Should journal and book titles in the CiteA, CiteB, ... CiteZ pages be italicized? — Alonso del Arte 15:56, 29 November 2011 (UTC)

Answer: I am continually adding items to the Cites pages. Each change calls for 4 clicks (preview,save,submit,approve), and each click takes several seconds. It is very slow work. Furthermore, I use the same line that I have typed when I add the work to the appropriate sequences in the OEIS entries. So I try to keep things as simple as possible. The line that I type has to work both on the wiki side, where the language is MediaWiki, and on the OEIS side, where the language is basically html, or plain text. So the answer to your question is, if you want to do it, go ahead. But I don't have time! N. J. A. Sloane, Oct 8, 2013.

Alright, I'll try to do it for CiteA tomorrow. Alonso del Arte 03:44, 25 August 2014 (UTC)


  1. (Done) Make the following replacements wherever the to-be-replaced string appears in an Author (%A) record of the database. Thanks! - Jon E. Schoenfield 01:24, 23 February 2015 (UTC)
    1. "Donald S. McDonald (don.mcdonald(AT)" -> "_Donald S. McDonald_" (none of these)
    2. "Donald S McDonald (don.mcdonald(AT)" -> "_Donald S. McDonald_" (none of these)
    3. "Randy L. Ekl (Randy.Ekl(AT)" -> "_Randy L. Ekl_"
    4. "R. H. Barbour (bbarbour(AT)" -> "_Robert H Barbour_"
    5. "Thomas Zaslavsky (zaslav(AT)" -> "_Thomas Zaslavsky_"
  2. (Done) Doublecheck numeric tables in Benford's law#Prime numbers and Benford's law. In regards to 1, the results are as I expected, but I'm doubting myself on 5, 6, 7. Alonso del Arte 03:44, 25 August 2014 (UTC)
  3. (Done) Replace "O. E. Pol" by "Omar E. Pol". Thanks in advance! - Omar E. Pol 14:30, 9 January 2014 (UTC)
    Seems done everywhere(?) except in REFS/LINKS where using only initials is the standard. MFH 23:15, 9 March 2014 (UTC)
  4. (Done) Replace "__Leroy Quet__" with "_Leroy Quet_". Thanks! - Jon E. Schoenfield 02:02, 11 February 2014 (UTC)
  5. (Done) Replace URL's or mark them with [broken link?] - R. J. Mathar 09:51, 11 July 2013 (UTC)
  6. (Done) Replace "outer shell" by "last section", except in the entry A173592. There are 44 sequences that contain this phrase. Thanks in advance! Omar E. Pol 13:10, 1 December 2013 (UTC)
    1. Completed the change with "outer shell" and "outer shells" then reverted A173592. The global replacement system isn't particularly flexible... Charles R Greathouse IV 18:39, 1 December 2013 (UTC)
  7. (Done) Request the deTeXification of "Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures". Search finds it 612 times. Peter Luschny 21:22, 17 November 2013 (UTC)
  8. (Done) Request the deTeXification of "Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al". Search finds it 628 times. Peter Luschny 23:19, 16 November 2013 (UTC)
  9. (Done) Replace "outer shell of the partitions" by "last section of the set of partitions". There are 74 sequences that contain this phrase. Thanks in advance! Omar E. Pol 11:46, 30 November 2013 (UTC)
  10. (Done) Request the following global replacements (each of which, the last time I checked, would cover 10 or more places in the OEIS). Thanks! Jon E. Schoenfield 05:09, 10 October 2013 (UTC)
    1. "Roberto E. Martinez II (remartin(AT)" -> "_Roberto E. Martinez II_"
    2. "Owen Whitby (whitbyo(AT)" -> "_Owen Whitby_"
    3. "Tomaz Pisanski (Tomaz.Pisanski(AT)" -> "_Tomaz Pisanski_"
    4. "T. D. Noe (" -> "_T. D. Noe_"
    5. "Pierre CAMI (colettecami(AT)" -> "_Pierre CAMI_"
    6. "Frans Faase (Frans_LiXia(AT)" -> "_Frans J. Faase_"
    7. "Rob Pratt (Rob.Pratt(AT)" -> "_Rob Pratt_"
    8. "Robert W. Pratt (Rob.Pratt(AT)" -> "_Rob Pratt_"
    9. "Howard A. Landman (howard(AT)" -> "_Howard A. Landman_"
    10. "Stephen Crowley (crow(AT)" -> "_Stephen Crowley_"
    11. "Richard Sabey (richardsabey(AT)" -> "_Richard Sabey_"
    12. "Olaf Voss (richyfourtythree(AT)" -> "_Olaf Voß_"
    13. "Greg Huber huber(AT)" -> "_Greg Huber_"
    14. "Jim Propp (propp(AT)" -> "_James Propp_"
    15. "Leonid Broukhis (leo(AT)" -> "_Leonid Broukhis_"
    16. "Neville Holmes (neville.holmes(AT)" -> "_W. Neville Holmes_"
    17. "Jonathan D. B. Hodgson (hodgsonjdb(AT)" -> "_Jonathan D. B. Hodgson_"
    18. "Leonid Broukhis (leob(AT)" -> "_Leonid Broukhis_"
    19. "Ignacio Larrosa Canestro (ignacio.larrosa(AT)" -> "_Ignacio Larrosa Cañestro_"
    20. "Ross Drewe (rd(AT)" -> "_Ross Drewe_"
    21. "Dann Toliver (fsdrt(AT)" -> "_Dann Toliver_"
    22. "_Mohammad K. Azarian_, azarian(AT)" -> "_Mohammad K. Azarian_"
    23. "Joel Lewis (jblewis(AT)" -> "_Joel B. Lewis_"
    24. "James East (jameseastseq(AT)" -> "_James East_"
    25. "Vassilis Papadimitriou (bpapa(AT)" -> "_Vassilis Papadimitriou_"
    26. "Paul Lusch (plusch(AT)" -> "_Paul Lusch_"
    Done. Charles R Greathouse IV 19:33, 12 October 2013 (UTC)
  11. (Done) Request the following global edits. Thanks! Jon E. Schoenfield 18:37, 4 October 2013 (UTC)
    1. change "Andre F. Labossiere (boronali(AT)" to "_André F. Labossière_"
    2. change "Bodo Zinser (BodoZinser(AT)" to "_Bodo Zinser_"
    3. change "Bodo Zinser (BodoZinser(AT)" to "_Bodo Zinser_"
    4. change "Henri Lifchitz 100637.64(AT)CompuServe.COM" to "_Henri Lifchitz_"
    5. change "Kailasam Viswanathan Iyer (kvi(AT)" to "_K.V.Iyer_"
    6. change "Sam Alexander (amnalexander(AT)" to "_Sam Alexander_"
    7. change "Soren Eilers (eilers(AT)" to "_Søren Eilers_"
  12. (Done) Go through the ~100 sequences in palindromic primes -keyword:base and give keyword:base to all appropriate sequences.
    About half needed the keyword. Charles R Greathouse IV 14:19, 3 October 2013 (UTC)
  13. (Done) Go through the 500+ sequences returned by searching for the email address "rpropper(AT)" and replace "Ryan Propper (rpropper(AT)" with _Ryan Propper_; make similar changes to remove email addresses of registered users Shyam Sunder Gupta (guptass(AT), Washington Bomfim (webonfim(AT), Augustine O. Munagi (amunagi(AT), Jud McCranie (JudMcCranie(AT), Omar E. Pol (info(AT), Mike Oakes (Mikeoakes2(AT), Robert Gerbicz (gerbicz(AT), Gene Ward Smith (genewardsmith(AT), Fred Schneider (frederick.william.schneider(AT), Ed Pegg Jr (ed(AT), and Clark Kimberling (ck6(AT)
  14. (Done) Request the following global edits:
    1. change "Michael Joseph Halm (hierogamous(AT)" to "_Michael Joseph Halm_"
    2. change "Howard A. Landman (howard(AT)" to "_Howard A. Landman_"
    3. change "R. H. Hardin rhh(at)" to "_R. H. Hardin_"
    4. change "Brendan McKay (bdm(at)" to "_Brendan McKay_"
    5. change "A. O. Munagi (amunagi(AT)" to "_Augustine O. Munagi_"
    6. change "Shyam Sunder Gupta (guptass(AT)" to "_Shyam Sunder Gupta_"
    7. change "Ryan Propper (rpropper(AT)" to "_Ryan Propper_"
    8. change "Jasinski Artur (grafix(AT)" to "_Artur Jasinski_"
    9. change "Artur Jasinski with assistance from Bob Hanlon (grafix(AT)" to "_Artur Jasinski_ with assistance from Bob Hanlon"
    10. change "Santi Spadaro (spados(AT)" to "_Santi Spadaro_"
    11. change "J. Lowell, jhbubby(AT)" to "_J. Lowell_"
    thanks! Jon E. Schoenfield 02:54, 3 October 2013 (UTC)
  15. (DONE) Change each of the ~83 sequences that contain the string "Diana Mecum (diana.mecum(AT)" and replace it with "_Diana L. Mecum_" (I'm assuming they're the same individual!). -- Jon E. Schoenfield, Sep 23 2013.
  16. (Done) Assuming that the email address and registered username in each of the following pairs is for the same individual, replace the existing name string (spellings may vary!) and existing email address with the registered username. -- Jon E. Schoenfield, Sep 23 2013.
    1. "cjsalves(AT)" / "_Carlos Alves_"
    2. "rpropper(AT)" / "_Ryan Propper_"
    3. "drew(AT)" / "_Andrew V. Sutherland_"
    4. "xordan.tom(AT)" / "_Tomas Xordan_"
    5. "rohelakhan(AT)" / "_Sameen Ahmed Khan_"
    6. "alonso.delarte(AT)" / "_Alonso del Arte_"
    7. "olivier.gerard(AT)" / "_Olivier Gérard_"
  17. (Done) Please replace everywhere:
    Thanks! Max Alekseyev 01:28, 27 September 2013 (UTC)
  18. (Done) Repair links to SeqFan threads as announced in Re: Early SeqFan archivesR. J. Mathar 18:04, 4 January 2013 (UTC)
  19. (Done) Replace "Vladeta Jovovic (vladeta(AT)eunet.yu)" by "_Vladeta Jovovic_" — Joerg Arndt 13:58, 21 May 2013 (UTC)
  20. (Done) Replace "Frank Ruskey, Nate Kube (ruskey(AT)" by "_Frank Ruskey_ and Nate Kube" . R. J. Mathar 14:13, 9 May 2013 (UTC)
  21. (Done) Replace the names "A simple regular expression in a labeled universe" by more specific ones. — R. J. Mathar 21:24, 17 November 2011 (UTC)
  22. (Done) The paper V. Jelinek, T. Mansour and M. Shattuck, On multiple pattern avoiding set partitions, Advances in Applied Mathematics Volume 50, Issue 2, February 2013, Pages 292-326 (I have a copy), contains a number of generating functions (See Theorems 4.1, 4.2, Ex. 4.16 (3), 4.17 (2), Prop. 4.20, 4.21, 4.23, 4.27, and maybe others). Could someone produce the sequences corresponding to these g.f.'s and add them to the OEIS if they are new, or add references to this paper if they are already in the OEIS? - N. J. A. Sloane, 1 January 2013. doi:10.1016/j.aam.2012.09.002, Theorem 4.1=A025242. Theorem 4.2=A005773. Ex. 4.16=A005183 and A116701, but H1121 gives negative terms (incorrect), L1121 =A209230 (new, sign corrected). L_{1232}=A005183, same as proposition 4.20. Lemma 4.21=essentially A132750. R. J. Mathar 21:42, 12 January 2013 (UTC)
  23. (Done) Replace by . R. J. Mathar 18:15, 8 January 2013 (UTC)
  24. (Done) Apparently the book M. Pitici, editor, The Best Writing on Mathematics, Princeton Univ. Press, 2012 mentions the OEIS - can someone tell me in which chapter, page numbers, etc.? - N. J. A. Sloane, Jan 02 2013
  25. (Done) Repair references to arxiv esp. by E. Deutsch: already fixed ~ 25 occurrences of "arxiv1111...." to "arxiv:1111..." by hand, but there are about 30 left (cf., and most probably others (not only(?) from the same submitter). — M. F. Hasler 18:37, 6 January 2013 (UTC)
    I corrected all 26 cases, plus two similar ones I found. Charles R Greathouse IV 18:10, 7 January 2013 (UTC)
  26. (Done) Apparently this paper: Keisuke Nakano, Shall We Juggle, Coinductively?, in Certified Programs and Proofs, Lecture Notes in Computer Science Volume 7679, 2012, pp 160-172, DOI 10.1007/978-3-642-35308-6_14 mentions the OEIS and probably has one or more new sequences in it - does anyone have access to a copy? - N. J. A. Sloane, Jan 02 2013
  27. (Done) Insert b-files at the top of the "links" field. If possible automatically move b-file links that are not at the top to the top. - Joerg Arndt 12:27, 25 April 2013 (UTC)
    Russ Cox revised program on Aug 12 2014 to take care of this for b-files. Thanks, Russ! Ray Chandler, Aug 24 2014.

See Suggested Projects/Archive for projects completed earlier.

Not done

  1. Reducing all (or most) b-files to the standard size (10000?). [From Moshe Levin]
    I strongly disagree. The b-files should never be shortened. — N. J. A. Sloane, Oct 25 2011
    Maybe extending when possible b-files to a thousand or ten thousand terms (as recently happened with A065449 with a b-file that went up to 466, so Charles extended it to 1000. [From Alonso del Arte 20:02, 24 October 2011 (UTC)]
    This has been discussed earlier, see also If there is an excessively large b-file, it would indeed be useful to have b-file(s) of handier size, which could be created by the server (either physically as a file or virtually/dynamically "upon request"), by simply truncating the existing one. — M. F. Hasler 19:59, 24 October 2011 (UTC)
  2. Add a link from to . Add a link from to . Add a link from to . - Omar E. Pol 12:15, 1 May 2014 (UTC) Why? Bookmarks exist. - Joerg Arndt 12:25, 30 June 2014 (UTC)

See also