Neil Sloane (home page)

Neil J. A. Sloane: Home Page

(May 2012) After 43 years I have now retired from AT&T. My new coordinates are:

Neil J. A. Sloane, Chairman, OEIS Foundation
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Email: njasloane@gmail.com
Home page: http://NeilSloane.com (this page)

Research interests: Mathematics, especially combinatorics, number theory, geometry, algebra;
communications, especially coding theory and quantization;
statistics, especially orthogonal arrays and the design of experiments.

OEIS	The OEIS Foundation	Gosset	Tables
Recent papers	Eternal Home Page proposal	Challenge Problems	Family
Publications (all)	Books	Patents	Coauthors
Awards	Press clippings	Pictures	Vita
Email: njasloane@gmail.com	On Facebook	On LinkedIn	Links

February 2 2023: OEIS Foundation Seeks to Raise $3M Endowment to Fund Full-Time Managing Editor. See Announcement.

June 27 2021, Russ Cox is new President of OEIS Foundation, I am Chairman of the Board. See Announcement.

Videos: 23 Youtube/Numberphile videos with Brady Haran (10.3 million views), About 23 other videos and slides of talks

Most recent talks

A Nasty Surprise in a Sequence and Other OEIS Stories, Talk in Doron Zeilberger's Experimental Math Seminar at Rutgers University, Oct 10, 2024 (my 85th b'day): Youtube video, Vimeo video, [The talk begins after about 60 seconds of confusion.] Slides, Another copy of slides.
Eric Angelini's Comma Sequence, Talk in Doron Zeilberger's Experimental Math Seminar at Rutgers University, January 18, 2024: Youtube video, Slides, Another copy of slides.
Pictures from 50 Years of the OEIS, Talk in Kansas State University Mathematics Department's Art and Mathematics Seminar, Nov. 2 2023: Video; Slides; Another copy of slides.
New Gilbreath Conjectures, Sum and Erase, Dissecting Polygons, and Other New Sequences, Talk in Doron Zeilberger's Experimental Math Seminar at Rutgers University, Sept. 14, 2023: Video (Youtube), Video (Vimeo), Slides; Postscript to talk (Last updated Sep 25 2023).

Most recent papers

Eric Angelini, Michael S. Branicky, Giovanni Resta, N. J. A. Sloane, and David W. Wilson, The Comma Sequence: A Simple Sequence With Bizarre Properties, arXiv:2401.14346, Jan 25 2024.
N. J. A. Sloane and Gavin A. Theobald, On Dissecting Polygons into Rectangles, arXiv:2309.14866 [math.CO], 2023.

"A Handbook of Integer Sequences" Fifty Years Later

2023 is the 50th anniversary of the publication of "A Handbook of Integer Sequences" (Academic Press, 1973), which listed 2,372 sequences. (Today, April 30 2023, after 50 years work by many thousands of people, the database contains 362,407 entries.)
I wrote an article "`A Handbook of Integer Sequences' Fifty Years Later", which can be seen on the arXiv (free, but lower quality figures), in the Mathematical Intelligencer on 17 April 2023 (html or pdf) (Open Access), and on my home page (which has the highest quality figures). This was followed by several other articles:
Most notably, Siobhan Roberts wrote an article "What Number Comes Next? Ask the Encyclopedia of Integer Sequences" for the New York Times, which appeared online on May 21 2023. It can be found on the New York Times online archive here, and there is also a copy on my home page here. It appeared in the print version of the New York Times in the Science Section on Tuesday, May 23 2023, with a slightly different title.
Manon Bischoff, The Most Boring Number in the World is ..., Scientific American, March 3 2023. (Originally appeared in Spektrum der Wissenschaft.)
The French website La Recherche did an interview with me (in French).
The French magazine Science et Avenir (on every newsstand in the French-speaking world) had an article about me in the April 21 2023 issue entitled "Les `nombres premiers de la Bête' et autres étrangetés mathématiques de l'encyclopédie des suites d'entiers". (I carefully chose a photo that doesn't look like me, because I didn't want people pointing at me next time I'm in France, and saying "He has the Number of the Beast".)
ThatsMaths, A Remarkable Sequence in OEIS, Sep 28 2023.
This reminded me that in 1987 James Gleick wrote an article "In a `random world', he collects patterns" about me which appeared on the front page of the New York Times Tuesday Science Section on January 27 1987 (Page 1 left, page 1 right, page 2 left, page 2 right, transcript).
There is also an older list of Press Clippings.

Recent papers

Brady Haran and N. J. A. Sloane, The Yellowstone Permutation, Numberphile video, Jan 29 2023.
N. J. A. Sloane, "A Handbook of Integer Sequences" 50 Years Later, Preprint, Jan 08 2023. Latest revision, Jan 17, 2023. (arXiv: http://arxiv.org/abs/2301.03149, Jan 16 2023)
Brady Haran and N. J. A. Sloane, "A Number Sequence with Everything" (the Inventory Sequence A342585), Numberphile video, November 2022.
Brady Haran and N. J. A. Sloane, Problems with Powers of Two, Youtube Numberphile Video, Sep 21 2022; STOP PRESS: Postscript to Problems with Powers of Two, Sep 21 2022. See A352178 for the latest results.
N. J. A. Sloane, New Sequence Problems and Solutions from 2022, Talk in Doron Zeilberger's Experimental Math Seminar at Rutgers University, Sept. 15, 2022; Youtube video, Slides
Michael De Vlieger, Thomas Scheuerle, R\'{e}my Sigrist, N. J. A. Sloane, and Walter Trump, The Binary Two-Up Sequence, arXiv:2209.04108, Sep 11 2022.
Blog: The Two-Up Sequence A090252, June 13 2022. I started a blog about a very interesting "Lexicographically Earliest" sequence A090252 that might be solvable with a collective effort. Many conjectures but few theorems. This blog is now frozen.
N. J. A. Sloane, The On-Line Encyclopedia of Integer Sequences: An illustrated guide with many unsolved problems, Guest Lecture given in Doron Zeilberger's Experimental Mathematics Math640 Class, Rutgers University, Spring Semester, Apr 28 2022: Video, Slides.
Max A. Alekseyev and N. J. A. Sloane, On Kaprekar's Junction Numbers, Journal of Combinatorics and Number Theory, 12.3 (2020) [2023], 115-155.
Brady Haran and N. J. A. Sloane, Stones on an Infinite Chessboard, Numberphile video, January 2022.
Brady Haran and N. J. A. Sloane, Most Wanted Prime, Numberphile video, December 2021.
N. J. A. Sloane, Lovely New Problems From the Past Months. Talk in Doron Zeilberger's Experimental Math Seminar at Rutgers University, Sept. 9, 2021; Video, Slides
N. J. A. Sloane, The OEIS: A Fingerprint File for Mathematics, article for "Early Careers" section of Notices of Amer. Math. Soc., 68:9 (October 2021), 1515-1516.

My current project (with Omar Pol and Hartmut Hoft) involves an object that fits in a corner, technically an encoignure. I wrote the following poem to show how to pronounce it.

Bad Furniture

The wardrobe has lost a lobe,
The blender has gone on a bender,
The pouf is rather uncouth,
The armoire is not for moi,
The icebox is full of rocks,
The credenza has influenza,
And worst of all,
The encoignure is full of manure.

Lars Blomberg, Scott R. Shannon, and N. J. A. Sloane, Graphical Enumeration and Stained Glass Windows, 1: Rectangular Grids, Preprint, revised May 21 2021. To appear in INTEGERS.
Lars Blomberg, Scott R. Shannon, and N. J. A. Sloane, Graphical Enumeration and Stained Glass Windows, Additional Illustrations for Part 1, Rectangular Grids, Preprint, May 24 2021.
M. Alekseyev, J. S. Myers, R. Schroeppel, S. R. Shannon, N. J. A. Sloane, and P. Zimmermann, Three Cousins of Recaman's Sequence, New version, May 29 2021, accepted for publication in Fibonacci Quarterly.
F. Michel Dekking, Jeffrey Shallit, and N. J. A. Sloane, Queens in exile: non-attacking queens on infinite chess boards, Electronic J. Combin., 27:1 (2020), #P1.52.
Eric Angelini, Lars Blomberg, Charlie Neder, Remy Sigrist, and N. J. A. Sloane, "Choix de Bruxelles": A New Operation on Positive Integers, arXiv:1902.01444, Feb 2019; Fibonacci Quarterly, 57:3 (2019), 195-200.
N. J. A. Sloane, The On-Line Encyclopedia of Integer Sequences, Notices, Amer. Math. Soc., 65 (No. 9, Oct. 2018), 1062-1074.
C. Goodman-Strauss and N. J. A. Sloane, A Coloring Book Approach to Finding Coordination Sequences, Acta Crystallographica Section A: Foundations and Advances, 2019, Volume A75, pages 121-134. Also on my home page. Also arXiv:1803.08530. [Last revised Jan 29 2019]
Moa Apagodu, David Applegate, N. J. A. Sloane, Doron Zeilberger, Analysis of the Gift Exchange Problem, 2017. Also arXiv:1701.08394, although the version on my home page may be more up-to-date. [Last revised Jan 30 2017]
Shalosh B. Ekhad, N. J. A. Sloane, and Doron Zeilberger, Automated Proofs (or Disproofs) of Linear Recurrences Satisfied by Pisot Sequences, 2016. Also arXiv:1609.05570, although the version on my home page may be more up-to-date. [Last revised Sep 27 2016]
Margaret Wertheim, The Fax Numbers of the Beast, and Other Mathematical Sports: An Interview with Neil Sloane, Cabinet Magazine, Issue 57, Spring 2015, pages 48-54.
Siobhan Roberts, How to Build a Search Engine for Mathematics: The surprising power of Neil Sloane's Encyclopedia of Integer Sequences, Nautilus Magazine, Issue 29, Chapter 4, Oct 22 2015.
Featured in Slashdot on August 7 2015.
Erica Klarreich, The Connoisseur of Number Sequences, Quanta Magazine, August 6 2015.
May 2015: Elected Fellow of The Learned Society of Wales (FLSW)
Shalosh B. Ekhad, N. J. A. Sloane, and Doron Zeilberger, Odd-Rule Cellular Automata on the Square Grid, 2015. Also arXiv:1503.04249, although the version on my home page may be more up-to-date. [Last revised Mar 20 2015]
Shalosh B. Ekhad, N. J. A. Sloane, and Doron Zeilberger, A Meta-Algorithm for Creating Fast Algorithms for Counting ON Cells in Odd-Rule Cellular Automata, 2015. Also arXiv:1503.01796, although the version on my home page may be more up-to-date. See also the accompanying Maple package. [Last revised Mar 05, 2015.]
N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, submitted to Ron Graham Festschrift, 2015. Also arXiv:1503.01168, although the version on my home page may be more up-to-date. [Last revised Mar 05, 2015.]
David L. Applegate, Hans Havermann, Bob Selcoe, Vladimir Shevelev, N. J. A. Sloane, and Reinhard Zumkeller, The Yellowstone Permutation, Journal of Integer Sequences, Vol. 18 (2015), Article 15.6.7; also arXiv:1501.01669 (JIS, arXiv, on my home page).
Poster I created to celebrate reaching 250,000 sequences; key to the poster.
OEIS-50 Conference. On October 9-10 2014 there was a conference at DIMACS, Rutgers University, to celebrate the 50th birthday of the OEIS, reaching 250,000 sequences, and my 75th birthday. Videos of the talks can be seen here
N. J. A. Sloane, A Note on Modular Partitions and Necklaces; Preprint, 2014 (mentioned in A047996 and A241926). [May 06 2014]
Claude Elwood Shannon: Miscellaneous Writings, edited by N. J. A. Sloane and A. D. Wyner, 1993, Deposited in The Library of Congress, The British Library, and the libraries of M.I.T., Cornell, Univ. Mich. and AT&T Bell Laboratories. October 15 2013: I have placed a copy on the Internet Archive - see archive.org/details/ShannonMiscellaneousWritings
N. J. A. Sloane, 2178 And All That, Fibonacci Quarterly, 52 (2014), 99-120. Also arXiv:1307.0453, although the version on my home page may be more up-to-date.
N. J. A. Sloane, Recent and Noteworthy Sequences in the OEIS. [Dec. 18, 2012]
N. J. A. Sloane, Recent and Noteworthy Sequences in the OEIS: The Illustrations. [Dec. 18, 2012]
B. Chaffin, J. P. Linderman, N. J. A. Sloane and A. R. Wilks, On Curling Numbers of Integer Sequences. [Dec. 25, 2012; Mar 12 2013]
N. J. A. Sloane, The On-Line Encyclopedia of Integer Sequences, Proceedings Fifteenth Conference on Fibonacci Numbers, Eger, Hungary, June 2012, Annales Mathematicae et Informaticae, 41 (2013) pp. 219-234.
Susanna Cuyler and N. J. A. Sloane, A Simple and Easily-Remembered Method for Solving the Rubik Cube, 2012. (An informal guide for distribution to friends.)
D. Applegate, M. LeBrun, N. J. A. Sloane, Dismal Arithmetic, J. Int. Seq., 14 (2011), #11.9.8.
D. Applegate, M. LeBrun, N. J. A. Sloane, Carryless Arithmetic, College Math. J., Vol. 43 (No. 1, 2012), pp. 43-50 (Special issue in honor of Martin Gardner), received 2013 George Polya Award from MAA; also arXiv:1008.4633.
N. J. A. Sloane, V. A. Vaishampayan, S. I. R. Costa, A Note on Projecting the Cubic Lattice, Discr. Comput. Geom., 46 (No. 3, 2011), 472-478.
D. Applegate, O. E. Pol, N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congress. Numer., 206 (2010), 157-191.
D. Applegate, N. J. A. Sloane, The Gift Exchange Problem, arXiv:0907.0513, slightly later version with typo corrected.
Eight Hateful Sequences, paper for the 8th Gathering for Gardner, revised Sept. 11, 2013 [old version: arXiv:0805.2128].
N. J. A. Sloane, V. A. Vaishampayan, Generalizations of Schöbi's Tetrahedral Dissection, Discr. Comput. Geom., 41 (No. 2, 2009), 232-248; arXiv:0710.3857.
C. Tian, V. A. Vaishampayan, N. J. A. Sloane, Constant Weight Codes: A Geometric Approach Based on Dissections, IEEE Trans. Inform. Theory, 55, (No. 3, 2009), 1051-1060; arXiv:0706.1217.
Seven Staggering Sequences, in Homage to a Pied Puzzler, E. Pegg Jr. et al. (eds.), A. K. Peters, Wellesley, MA, 2009, pp. 93-110; arXiv:0912.2394.

Other recent highlights

The OEIS appears (under 1973) in WolframAlpha's Timeline of Systematic Data and the Development of Computable Knowledge, which extends from cave paintings to the present day. [Oct 14 2011]

Nov 11 2010: The new version of the OEIS is launched! For almost two years now, I have been trying to convert the On-Line Encyclopedia of Integer Sequences (OEIS) to a version that will run independently of me, and to find a permanent home for it, not on my home page. The first step was to set up a non-profit foundation to own, maintain and collect funds to support the OEIS: this was completed in 2009 - see The OEIS Foundation web site.
The second step was to set up a version of the OEIS which would run autonomously on a commercial web site, operating as a moderated wiki, and controlled by a board of editors. Unfortunately, 18 months ago we discovered that the standard mediawiki software was incapable of handling the kind of queries that the OEIS generates. This problem seemed unsurmountable, and I had almost given up hope that it would ever be solved.
But thanks to the enormous efforts of Russ Cox, who has completely rewritten all the OEIS software, the new OEIS was launched on Nov 11 2010. David Applegate has also been of great help in getting the new system working. At the time of the launch, the OEIS contained 180284 sequences. This means that after 46 years, I no longer have to process every single contribution to the database. Thank you, Russ and Dave: you have saved the OEIS!
The URL for the new OEIS is oeis.org. I recommend that before using it, you first register at oeis.org/wiki. When you get issued a password, go to the main page and login with the same user name and password.
Now when you look at a sequence, you will see "history" and "edit" buttons next to the "graph" and "listen" buttons. The "edit" button lets you edit the sequence. To submit a new sequence, use the "Submit new seq." link at the bottom of any sequence page. All contributions will be reviewed by the editors (if you would like to help by becoming an editor, let me know - we need more editors!).

The OEIS Movie! To celebrate the launching of the OEIS Foundation, Tony Noe has made a movie showing the first 1000 terms of 1000 sequences, with soundtrack from Recaman's sequence A005132. The best way to watch it is to first download the file from Tony's web site, http://www.sspectra.com/math/OEISMovie.mov and then play it with QuickTimePlayer 7.

The list of works that reference the OEIS is continually being updated. As of June 2015 there are over 4200 citations.

Tables

Papers and Books Grouped by Subject: (Most of these pages need to be updated.)