Goals of The OEIS Foundation Inc. The OEIS Foundation Inc. is a New Jersey nonprofit corporation (#0101000611; Articles of incorporation filed with the State of New Jersey, April 14 2009; EIN 30-0562250) whose main goals are the following four items: To own the intellectual property known as "The On-Line Encyclopedia of Integer Sequences®" (or "OEIS®"). To maintain the OEIS as a service that is freely accessible by the general public. To act so as to maintain its own existence indefinitely. To collect and distribute funds in order to carry out the first three goals. These goals are described in greater detail in a later section of this web page, and in the Articles of Incorporation and Bylaws. To facilitate the fourth goal, The OEIS Foundation Inc. has been approved by the Internal Revenue Service as a charity and a Section 501(c)(3) tax-exempt organization. For details please see the section on Tax-exempt status. Tax-deductible donations to The OEIS Foundation Inc. can be made through PayPal using the icon at the top right of this page (see also below). Note: Except when used in the name of this corporation (The OEIS Foundation Inc.), the word "OEIS" is an abbreviation for "The On-Line Encyclopedia of Integer Sequences®".

Description of The On-Line Encyclopedia of Integer Sequences® (or OEIS®) The On-Line Encyclopedia of Integer Sequences® (OEIS®) is the on-line version of a database of sequences of numbers which will soon be celebrating its 50th anniversary. A conventional dictionary is a collection of words, together with explanations of their meanings, hints for their pronunciation, pictures illustrating particular words, examples showing how the words have been used in books and newspapers, and so on. The OEIS is a collection of sequences of numbers (such as 1, 2, 4, 8, 16, 32, 64, 128, ...) together with, for each sequence, a list of items such as: The first 10, or 10,000, or sometimes 500,000 terms of the sequence

A definition or description of the sequence

Comments explaining further properties of the sequence

Formulas for generating the sequence

Computer programs for generating the sequence

References to books and articles where the sequence has appeared

Links to web pages on the Internet where the sequence has appeared

Cross-references to related entries in the OEIS

The name of the person who submitted the sequence to the OEIS

Further names of people who have added additional information about the sequence

Examples illustrating some of the terms of the sequence (for example, sequence A124. which gives the maximal number of pieces that can be obtained when cutting a circular pancake with n cuts, is illustrated with pictures showing the pieces obtained with n = 1, 2, 3, 4 and 5 cuts)

The history of each sequence in the OEIS as it has evolved over time

Users of the OEIS may also view graphs or plots of each sequence, or to listen to the sequence when it is converted to music The OEIS currently contains about 300,000 entries (although that number will be out-of-date by the time you read it). These have been distilled from many sources - books, journals, articles, and letters and electronic mail messages from thousands of contributors. Since November 11, 2010, users have been able to use the Internet to submit contributions to the OEIS. All submissions are refereed.

How the OEIS is used The main use for the OEIS is to identify a number sequence that you have come across, perhaps in your work, while reading a book, or in a quiz, etc. For example, you discover what you think may be a new algorithm for checking that a file of medical records is in the correct order. (Perhaps you are a computer scientist or someone working in information science.) To handle files of 1, 2, 3, 4, ... records, your algorithm takes 0, 1, 3, 5, 9, 11, 14, 17, 25, ... steps. How can you check if someone has discovered this algorithm before? You decide to ask the OEIS if this sequence has appeared before in the scientific literature. You go the OEIS web site, enter the numbers you have calculated, and click "Submit". The reply tells you that this is sequence A3071, which is the number of steps needed for "sorting by list merging", a well-known algorithm. The entry directs you to Section 5.3.1 of Volume 3 of D. E. Knuth, "The Art of Computer Programming", where you find your algorithm described. The entry even gives an explicit formula for the nth term. You decide not to apply for a patent! The OEIS web site includes a list of some 4500 articles, books, theses, etc., that have acknowledged help from the OEIS. For further information about the OEIS, see the OEIS Welcome Page, the Lookup Page, the Demonstration Pages, or the Wikipedia article.

History of the OEIS The collection was begun by Neil J. A. Sloane (henceforth, "NJAS") in 1964 when he was a graduate student at Cornell University in Ithaca NY. He had encountered a sequence of numbers while working on his dissertation, namely 1, 8, 78, 944, ... (now entry A435. in the OEIS), and was looking for a formula for the n-th term, in order to determine the rate of growth of the terms. He noticed that although several books in the Cornell library contained sequences somewhat similar to this, this particular sequence was not mentioned. In order to keep track of the sequences in these books, NJAS started recording them on file cards, which he sorted into lexicographic order. The sequences were transferred to punched cards in 1967, and were made into a book in 1973 ("A Handbook of Integer Sequences", by NJAS, Academic Press, NY). NJAS joined AT&T Bell Laboratories in 1969. Following the publication of the book, a large amount of correspondence ensued, with suggestions for further sequences and updates to the existing entries. Many people remarked how useful they found the book, and how surprising it was that no one had published such a collection before. By the early 1990's over a cubic meter of of correspondence had accumulated. A Canadian mathematician, Simon Plouffe, offered to help in preparing a revised edition of the book, and in 1995 "The Encyclopedia of Integer Sequences", by NJAS and Simon Plouffe, was published by Academic Press, San Diego. (Simon Plouffe is now one of the Trustees of The OEIS Foundation Inc.) The 1973 book contained 2372 sequences, and the 1995 book 5487 sequences, occupying 587 pages. Again, once the book appeared, many further sequences and updates were submitted from people all over the world. NJAS waited a year, until the size of the collection had doubled, to 10,000 entries, and then in 1996 he launched the On-Line Encyclopedia of Integer Sequences on the Internet. From 1996 until November 11, 2010, this was part of NJAS's home page on the AT&T Labs Web Site. Since 1996, the collection has grown by 10,000 to 18,000 entries per year. At the present time (May 29, 2013) there are 225,735 entries. If it were to be published in book form today, it would require at least 750 volumes the size of the 1995 book. Starting in 2002, NJAS added a group of associate editors to help process submissions to the OEIS. However, because they did not have access to the computer where the OEIS was maintained, almost all the work of updating it had to be done single-handedly by NJAS. This involved processing 100 or 200 emails every day, and was getting to be beyond what one person could handle. In January 2009, therefore, it was decided to make a drastic change. We (NJAS and the associate editors) made a plan to convert the OEIS into a "wiki" format, somewhat along the lines of the well-known Wikipedia, which would be hosted by a commercial hosting service. (A copy of a letter of consent from AT&T agreeing to this course of action is available on request from NJAS.) It was also decided to set up the OEIS Foundation, the goals of which would be to own, maintain and raise funds to support the new version of the OEIS. Most of this went smoothly. The OEIS Foundation Inc. was incorporated in the State of New Jersey on April 14, 2009. We rented space on a commercial hosting service, and tried to move the OEIS to the new site. Here, however, we ran into a very serious problem. In the summer of 2009, when we tried to get the OEIS working as a wiki, we discovered that the Mediawiki software was not capable of handling the kind of queries that arise in looking up sequences. This was a disaster. It took us over a year to resolve this problem. In the end, Russ Cox completely rewrote all the programs needed to maintain the database and answer queries - a huge task! NJAS's colleague David Applegate has also been of enormous help in getting the new system working. As a result of their work, the new OEIS was finally launched on November 11, 2010. (For more details, see the attached announcement.) It is now possible for anyone in the world to propose a new sequence or an update to an existing sequence. To do this, users must first register. A group of about 130 editors has been formed, whose job it is to review submissions before they become a permanent part of the OEIS. So, after nearly two years of struggle, the OEIS was finally able to operate without NJAS having to approve every change. After 46 years of running the database, this came as a great relief to him.

The new OEIS As mentioned in the previous paragraph, the OEIS was successfully launched in its new home (http://oeis.org) on November 11, 2010. At this time it contained 180,284 sequences. In the first full year of operation, from Nov 11 2010 to Dec 1 2011, 19716 new sequences were accepted, an average of over 50 per day, and there were about 250 edits per day of existing sequences.

We now have over 20 Editors-in-Chief and over 80 Associate Editors, and about 2000 registered users (see here for these lists). The following is a summary of the traffic on the new web site for the months of December 2010 and September 2015. The first four columns are the daily average, the last six columns are the total for the month. (These figures don't mean much, since most of the traffic comes from web-crawlers, but are shown here because people often ask for them. The figures are lower for 2015 presumably because now the web-crawlers are only downloading pages that have changed.) Hits Files Pages Visits | Sites KBytes Visits Pages Files Hits 164491 93721 141310 8290 | 84612 40341570 257006 4380636 2905370 5099232 71347 69146 34105 1182 | 12236 11502230 26021 750326 1521224 1569648 The Wiki part of the new OEIS can be found at http://oeis.org/wiki. Sequence A200000 was added on November 20, 2011: this is an interesting sequence concerning paths (or "meanders") through a grid. We reached 200000 sequences at midnight on December 1, 2011, the 200000-th sequence being A201463: see the Press release. In December 2014 the editors voted on which recently submitted sequence would become A250000. The winner was the Peaceable Queens sequence, originally submitted by Don Knuth on August 1, 2014, and renumbered as A250000 on December 15 2014.

Further details about the goals of The OEIS Foundation Inc. The goals are repeated here, giving further details about each one. (1) To own the intellectual property known as "The On-Line Encyclopedia of Integer Sequences" (or "OEIS"). Added October 28, 2009: NJAS has now transferred his intellectual property in the OEIS to The OEIS Foundation Inc. For details see below. (2) To maintain the OEIS as a service that is freely accessible by the general public. The new version of the OEIS launched on November 11, 2010 (see the announcement) can be accessed on the Internet free of charge by anyone in the world. It has the form of a "moderated wiki". Any registered user (and registration is free) can propose new sequences or modifications to existing entries. However, these proposals will not become a permanent part of the OEIS until they have been approved by a member of the Editorial Board.

People without access to the Internet can consult the OEIS via two free email services. One of the responsibilities of The OEIS Foundation Inc. is to keep the new version of the OEIS, (or, in future years, whatever replaces it) up and running 24 hours a day, seven days a week. This will of course require maintaining all the computer programs that underlie the OEIS. (3) To act so as to maintain its own existence indefinitely. The trustees are to serve for a period of three years, with the option of unlimited renewals. The trustees are to elect the officers, and new members may be added as the needs of the OEIS evolve. The trustees are also to monitor the performance of the Editorial Board of the OEIS. It is hoped that the OEIS will survive into the distant future, and the Trustees of The OEIS Foundation Inc. are charged with taking "the long view". This will include evolving the medium in which the OEIS is stored when that becomes necessary. Over the past 46 years the medium in which the OEIS has been stored has changed from file cards to punched cards to magnetic tape to magnetic disks, and no doubt further changes will be required in the future. A list of members of the Board of Trustees may be found here. (4) To collect and distribute funds in order to carry out the first three goals. It is intended that The OEIS Foundation Inc. will be a charity and a Section 501(c)(3) tax-exempt organization. An application for tax-exempt status was filed with the Internal Revenue Service on July 2, 2009. Tax-exempt status was granted on September 10, 2009 (see the following section). Initially the expenses will be the costs involved with setting up The OEIS Foundation Inc., filing for tax-exempt status, and in maintaining the wiki version on a web hosting site. Additional expenses will arise from publicizing the Foundation at scientific meetings. Future expenses may include paying salaries to people to maintain the OEIS.

The OEIS Foundation Advisory Board The OEIS Advisory Board was created on May 7, 2013, with the goal of having a group of distinguished scientists that the Board of Trustees and other members of the OEIS community can call upon for advice and guidance on matters related to the OEIS or the OEIS Foundation. A list of the members of the Advisory Board may be found here. The Advisors will be invited to participate in meetings of the Board of Trustees, and to vote on resolutions, although their votes will not be counted in the official tally. To begin with, members may be added to or removed from the Advisory Board by the President after consultation with the Board of Trustees. Initially there will not be a fixed term for Advisory Board members. At some later time, the make-up of the Advisory Board may be added to the By-Laws.

Tax-exempt status and other legal documents We applied for tax-exempt status in the USA for The OEIS Foundation Inc. on July 2, 2009. Here is a copy of the IRS Form 1023 that we submitted, and of an attachment containing detailed responses to certain sections of that form. On August 22, 2009, we received a letter from the IRS requesting additional information and clarification of certain points. Neil J. A. Sloane replied on August 26, 2009, providing answers to these questions. His letter can be seen here. On September 10, 2009, the IRS approved our request. Their letter can be seen here. The important points are as follows: The OEIS Foundation's tax identification number or EIN is 30-0562250.

Effective Date of Exemption: April 14, 2009. Accounting Period Ending: December 31.

The OEIS Foundation Inc. is exempt from Federal income tax under section 501(c)(3) of the Internal Revenue Code.

Contributions to the Foundation are deductible under section 170 of the Code.

The Foundation is also qualified to receive tax deductible bequests, devises, transfers or gifts under section 2055, 2106 or 2522 of the Code.

The IRS has determined that the Foundation is a public charity under section 170(b)(1)(A)(vi) of the Code. We are very grateful to Nancy Eberhardt, Esq., Director of the New Jersey Program of the Pro Bono Partnership, for her invaluable help with all the legal matters involved in setting up and registering the OEIS Foundation. The New Jersey Pro Bono Partnership has also been of great help in putting us in touch with attorneys who have assisted us in drafting legal documents that we needed for our web site. Several times now we have asked Nancy Eberhardt Esq. and the New Jersey Pro Bono Partnership for help, and they have never let us down. We also thank Terry Ilardi, Esq., Copyright Counsel for the IBM Corporation (working "Pro Bono") who drafted our first two license agreements for us: the OEIS Contributor's License Agreement and the OEIS End-User License Agreement. The OEIS Foundation is very grateful to him for his help. We also thank Shannon Hennessy Pulaski, Esq., of Shannon Hennessy Pulaski, LLC (working "Pro Bono") who drafted the OEIS Terms of Use Agreement. The OEIS Foundation is very grateful to her for her help.

Transfer of IP in OEIS to The OEIS Foundation Inc. The following is a slightly edited version of an announcement that NJAS made on October 27 2009 to the Trustees of The OEIS Foundation Inc. Yesterday (Monday, October 26 2009) was a landmark day in the history of the OEIS. I transferred the intellectual property I own in the OEIS to The OEIS Foundation Inc. The letter of assignment can be seen here. To make the transfer precise, my colleague David Applegate and I burned a DVD containing a snapshot of the whole OEIS (the sequences, of course, as well as all the associated files), which accompanies the letter of assignment as Exhibit A. The DVD contains about 1.4GB. The main sequence file contains 164891 sequences. It is 2510785 lines long and contains 169521003 characters. There are also 10716 b-files, and the b-files and other similar files comprise 852M. Another 280M are files associated with the lookup process. I am grateful to Terry Ilardi, Esq., of IBM Corporation (working "Pro Bono") who drafted the letter of assignment, and to David Applegate for help in creating the DVD.

Trademarking "OEIS" On June 16, 2010, we filed applications to trademark "The On-Line Encyclopedia of Integer Sequences" and "OEIS" with the United States Patent and Trademark Office. We are very grateful to Debra A. Shelinsky Greene, Esq., Counsel, and Florence M. Niel Henits, Trademark Paralegal, both of the Trademarks and Copyrights division, Merck & Co., Inc., working "Pro Bono", who filed the applications on behalf of The OEIS Foundation. "OEIS" was registered on February 8, 2011, as a United States Trademark (Registration Number 3,916,748). In the TESS Database, it has serial number 85064211. A copy of the certificate can be seen here. The Reverse side of Certificate of Registration lists requirements that we must fulfill during 2011-2021. See Annual reminders. "THE ON-LINE ENCYCLOPEDIA OF INTEGER SEQUENCES" was registered on December 20, 2011, as a United States Trademark (Registration Number 4,072,712). In the TESS Database, it has serial number 85064202. A copy of the certificate can be seen here. The Reverse side of Certificate of Registration lists requirements that we must fulfill during 2011-2021. See Annual reminders. The "Continuing Use" certification of the Trademark "OEIS" was accepted by the United States Patent and Trademark Office on May 25, 2016, and of the Trademark "THE ON-LINE ENCYCLOPEDIA OF INTEGER SEQUENCES" on April 11, 2017. We are very grateful to Merck & Co., Inc., and in particular Denise Maistickle and Nancy Rowe of the Merck Office of General Counsel, working "Pro Bono", who submitted these certifications on behalf of the OEIS Foundation. We also thank Nancy Eberhardt and Kate Marchese of the New Jersey Program of the Pro Bono Partnership for helping to bring this about. Trademark registrations in the US last for 10 years so therefore our trademark renewals for our two existing trademark registrations are not due until Feb 8, 2021 for OEIS and Dec 20, 2021 for THE ON-LINE ENCYCLOPEDIA OF INTEGER SEQUENCES. (Beware of scams that try to tell us they are due for renewal before those dates.)

The Fundraising Committee At the Board of Trustees meeting on June 8, 2010, it was unanimously agreed to establish a Fundraising Committee. The goal of the committee is to raise money to support the OEIS Foundation and the On-Line Encyclopedia of Integer Sequences (the OEIS). In particular, the goals of the Fundraising Committee are, first, to raise funds to to cover the day-to-day expenses of running the OEIS, and, second, to build up a reserve fund to ensure the long-term stability of the OEIS. The Board of Trustees agreed to adopt the term "Advisor" to refer to people who actively participate in fundraising or make similar contributions to the operation of the OEISF, but aren't necessarily Trustees of the OEIS Foundation or Editors of the OEIS. Committee members shall be appointed by the President of the OEIS Foundation, and members shall serve for two years, unless reappointed. The initial committee was formed on August 29, 2010. At the present time (Feb 16 2018), the Fundraising Committee consists of Charles Greathouse (Chair and OEIS Foundation Vice-President), Robert Price (OEIS Foundation Treasurer), Neil Sloane (OEIS Foundation President), and Susanna Cuyler (OEIS Foundation Secretary).

To donate to The OEIS Foundation Inc. Donations to The OEIS Foundation Inc. (tax-deductible in the USA) can be made in three ways: Through PayPal, using the icon at the top right of this page.

Directly, with a check or money order made out to The OEIS Foundation Inc., and sent to: Robert Roy Price,

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2340 Saunders Station Road,

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Directly, by a wire transfer to the OEIS Foundation bank account. For information on how to do this, please contact Robert Roy Price (treasurer(AT)oeisf.org) or Neil J. A. Sloane (president(AT)oeisf.org). Keep in mind that many corporations have a fund-matching program - they will match your charitable contributions. This is an excellent way to double your donation to the OEIS Foundation! All donations will be gratefully acknowledged on this page. The OEIS Foundation's tax identification number or EIN is 30-0562250.

List of donors to the OEIS Foundation Inc. Donors in 2020 Donations received in our 2019 fund-raising drive during the first ten days of January 2020 were included in our 2019 Donors list. Gauss Circle Benefactors in 2020 (Gifts of $25000 and above): Benefactors in 2020 (Gifts of $5000 and above): Sponsors in 2020 (Gifts of $1000 and above): Susanna Stevens Cuyler Google Inc. Hawaii Community Foundation Donald and Jill Knuth N. J. A. Sloane Allen Stenger Paul K. and Bonita K. Stockmeyer via the Heartland Charitable Trust Patrons in 2020 (Gifts of $100 and above): Jean-François Alcover Jerzy Borysowicz Donald Craig Petros Hadjicostas Richard Peterson Sinan Taifour Allan Wechsler Blake White Gregory Whittaker Stephen Wilkus Doron Zeilberger (in honor of Carsten Schneider who met a challenge made here) Doron Zeilberger (in honor of Chaim Even-Zohar who met a challenge made here. Jason Zimba Friends in 2020 (Gifts of less than $100): Amazon Smiles Peter Anderson Gabriel Apolinario Ball Corporation Malachi de AElfweald Marc Donis Michael Fernandez Darren Golbourn Ricado Grant Alan Gutzeit Peer Henselmans Deidre Denise House Viktar Kapelka Walter Kehowski Karl Keller Roger LeMesurier Metron Inc. David Pasino Thomas Poulos Raul Prisacariu Adrian Riekert Richard Ripert Rocrof Jonathan Skinner Pontus Sundqvist Liam Tarr Other gifts in 2020: The OEIS Foundation Inc. is also grateful to the American Mathematical Society for facilitating our access to MathSciNet in 2020. Donors in 2019 (including some from early January 2020) Gauss Circle Benefactors in 2019 (Gifts of $25000 and above): The Simons Foundation Benefactors in 2019 (Gifts of $5000 and above): Sponsors in 2019 (Gifts of $1000 and above): Anonymous Benevity Fund (includes several separate donations) Russ Cox Susanna Stevens Cuyler Harvey P. Dale Tom Duff Fred Kline Donald and Jill Knuth N. J. A. Sloane Allen Stenger Diana Wyant Patrons in 2019 (Gifts of $100 and above): Roland Acra Ian Agol and Michelle McGuinness Jean-François Alcover Lorenzo Sauras Altuzarra Anonymous David Applegate and Barbara Chubb Family Fund Gary Au Peter Bala Vasily Bashilov George Beck Benevity Fund Sara Billey Gerold Br%auml;ndli David Callan Ray Chandler Johann Cigler William Clary Matthew Conroy Claudio Corbetta Donald Craig Geoffrey Critzer Robert Dickau Susan Dickey Patrick Ekman Georg Fischer Daniel Frohardt Olivier GERARD Juri-Stepan Gerasimov Google Matching Fund Keith E. Gorlen Ron Graham Gregg-Springer Work via Fidelity Charitable Petros Hadjicostas Brian Hayes Paul Henry David Hruska Thomas Hull Daniel Kabat Peter Kagey Clark Kimberling Charles Kusniec Marc LeBrun Philip Lucido Seiichi Manyama Peter Mao James McCarron Danilo Merelli Joseph Moser William Muller Francois Oger Laurent Orseau Valentin Ovsienko James Rasbold Jon E. Schoenfield Bernard Schott Christopher Scussel Scott Shannon The John M. Shapiro Charitable Trust Louis Shapiro Rémy Sigrist Sven Simon John Snyder Colin Paul Spears Katherine Stange Richard P. Stanley / Stanley Family Fund / Fidelity Charitable Paul K. and Bonita K. Stockmeyer Symantec Corp. Matching Fund Robert Underwood Elizabeth Uptegrove Vinay Vaishampayan Willy Van den Driessche Tynan Wait Blake White Jesus Maria Yurramendi Mendizabal Celia Zeilberger (in honor of her father's 69th birthday) Doron Zeilberger (in honor of Marcus Michelen who solved a problem posed here) Friends in 2019 (Gifts of less than $100): Amazon Smiles (multiple donations) Matthew Anderson Samuel Anderson Éric Angelini Anonymous Alford Arnold Andrew Austin Arvind Ayyer in honour of Doron Zeilberger's 70th birthday Mohammad K. Azarian Marilena Barnabei Paul Barry Donatien Bénéat Benevity Fund (several separate donations) Emery Berger Bence Bernáth Swapnil Bhatia Jerzy Borysowicz William Bredbenner Sebastien Brisset Moren Brøns-Pedersen Pedro Caceres Andrew James Carr Alexandre Solé Carretero Alexis Chazard Bhadrachalam Chitturi Andres Cicuttin Lieven Clarisse Michael Collins Aldo Conca Ricardo Conceicao John Corbett Gary Croft Ingrid Daubechies Malachi de AElfweald Salvatore Di Guida Matthew Downey Greg Dresden Richard Drexel Abhinandan Dubey Stephen Dunn Silvain Dupertuis Nelano East Cole Ellis John Erickson Richard Farnhammer Mauro Fiorentini Peter Franklin Freeman-Mosher Family Fund Cezar Freitas Darren Golbourn Ricado Grant Dorian Greer Matthew Grimm Alan Gutzeit Hako Mark Hardman Mitchell Harris Robert Harris Kern Hast Kenneth Hawes John Hawkins Victor Hedwig Richard Hensh Paul Hewitt Frank Heyder Daniel Hoyt Nick Hunter-Jones Ioannis Iglezakis Cornel Izbasa Frank M. Jackson William Jackson Sudhir Jha Timothy Johnson D. B. Johnson-Davies V. P. Johnson Dmitri Kamenetsky Walter Kehowski Nitadori Keigo John Keith Al Kelley Sean Kenny Johann Klähn Warren W. Kokko Scott Kominers Marcin Konowalczyk Leonid Kovalev Jacek Kowalski Awani Kumar Michael Kuyumcu Wolfdieter Lang H. Leenman Ken Levasseur Hauke Löffler Robert Lyons Richard Mabry Joseph Maddocks Mehrad Mahmoudian Ivan Malopinsky Owen Mann Geoffrey Marnell L. Marshall McCloskey M. D. McIlroy Patrick McNab Euan McQuade Merzon Gregory Lloyd Mitchell Koji Miyazato Jamie Morken Richard Morris Kent Morrison William Muller Manfred Müller-Späth Nicely Done LLC Jeppe Stig Nielsen "None" Stephen Oberholtzer Kyle Ormsby Allyson Orourke-barrett Friedrich Pagenkopf Kaupo Palo John Peponis Raul Prisacariu Chamu Rajasekera Christopher Reade Wendy Reed Laurence Reeves Joseph Rickard Sean Riedel Manda Riehl Rocrof Rainer Rosenthal Martin Round Luc ROUSSEAU Andrey Rukhin Siddhant Saraf Metin Sariyar Lydia Schiff Julius Schmerling Gunther Schrack Andrew Schulman Brian M. Scott Paolo Sentinelli Dmitry Shemetov Geoffrey Shoesmith Nicholas Singer SMARTEC S.A.R.L. Kyle Smith Saul Spatz Samuel Spiro Christopher Stainsby John Stebbins James Stein Ralf Steiner Einar Steingrimsson John Stevens Andreas Stiller Fabian Stroh Daniel Suteu Hal Switkay David James Sycamore Plamen Tanovski Albert ten Oever uClassify Aleksei Udovenko Michael Ulm Mathijs van Meerkerk Stan Wagon Brandon Walker Blake White Wild Egg Pty Ltd Maxime Wybouw XU Pingya Magdalena Zarych Noam Zeilberger Other gifts in 2019: Peter Luschny kindly produced the new banner that appears on every OEIS page. The OEIS Foundation Inc. is also grateful to the American Mathematical Society for facilitating our access to MathSciNet in 2019. Donors in 2018 Gauss Circle Benefactors in 2018 (Gifts of $25000 and above): The Simons Foundation Benefactors in 2018 (Gifts of $5000 and above): N. J. A. Sloane Sponsors in 2018 (Gifts of $1000 and above): Russ Cox Susanna Stevens Cuyler Harvey P. Dale Tom Duff Google Matching Fund Fred Kline Donald and Jill Knuth Allen Stenger Seth A. Troisi Patrons in 2018 (Gifts of $100 and above): Jean-François Alcover Anonymous (2 donations) David Applegate Peter Bala George Beck Sarah Billey Sean Bloomfield Umberto Cerruti Benjamin Chaffin Ray Chandler Claudio Corbetta Donald Craig Emeric Deutsch (2) Robert Dickau Karl Dilcher REMI EISMANN Roger Entringer Georg Fischer Olivier GERARD Juri-Stepan Gerasimov Mats Granvik Petros Hadjicostas Brian Hayes Paul Henry David Hruska Thomas Hull Intel Matching Fund Karl Javorszky L. Edson Jeffery David Jeschke Peter Kagey Kirill Katsnelson Clark Kimberling Philip Lucido Keith F. Lynch Seiichi Manyama Peter Mao Charles F. Marion Jerry Metzger Microsoft / Benevity Community Impact Fund Cleve Moler Joseph Moser Enrique Navarrete Gordan Palameta Robert Price Klaus PURATH Paul Raff James Rasbold Matthew Roughan Jon E Schoenfield Christopher Scussel Shoichiro Sekiguchi The John M. Shapiro Charitable Trust Louis Shapiro REMY SIGRIST Sven Simon Todd Simpson Paul Stahura Richard P. Stanley / Stanley Family Fund / Fidelity Charitable Paul K. and Bonita K. Stockmeyer Symantec Corp. Mauro Torelli (in memory of Ottavio M. D'Antona) Elizabeth Uptegrove Jutta Wait Doron Zeilberger (in honor of Paul Johnson for answering a question raised here) Doron Zeilberger (in honor of Matthew C. Russell) Doron Zeilberger (in honor of Christopher Ryba for answering a question posed here) Doron Zeilberger (in honor of Will Sawin for answering a question posed here) Friends in 2018 (Gifts of less than $100): Aditya Akula Amazon Smiles (2 contributions) Peter Anderson Alexei Angelides Anonymous Thomas Anton Mohammad K. Azarian Marilena Barnabei Brian Beach Carlo Beenakker David Bell Benevity Fund (5 separate donations) James Bergen FRANCOIS BIENVENU Ethan Bolker Jerzy Borysowicz Robert Bryan Pedro Caceres Xiangyu Cao David Cerna Matthew Charnley Andres Cicuttin William Collier Jordan Combs David Crookes Árni Dagur Matthew Day Malachi de AElfweald Joseph Deutsch Martin Dimov Stephen Dunn Michel DUTEIL John Erickson Jonathan Evanson ROBERT FERREOL Pierandrea Formusa Nathan Fox Freeman-Mosher Family Fund Reza Ghazi Juan Gil Darren Golbourn Richard Grafen Charles Greathouse Merzon Grigory Andreas Grube Rainer Grzybowski Jacob Harder Konrad Harley Mitchell Harris Steven Harvey Peer Henselmans Enrique Pérez Herrero Greg Huber Sergey Ivanov Frank M Jackson Tom Jackson Leandro Junes Thomas Kahle Tamas Kalmarnagy Grace Kamau Amrish Kelkar Tanya Khovanova Steven Kifowit Ronald Kiszlowski James Knapp Shara Lalo Zagros Lalo Wolfdieter Lang Victor Lecomte Samuel Lerma Jack Levy Alan Listoe Chris Lombardi Nick MacKinnon Judson McCranie Gerald McGarvey Microsoft Matching Fund Kerry Mitchell Kent Morrison David Nacin Network for Good Nicely Done, LLC David Pasino Andrzej Perlanski Richard Peterson Arun Philip Henry Powell Krijn Reijnders Rocrof Louis ROGLIANO Fabian Röling Sven Ronnback Rainer Rosenthal Anna Roth Luc ROUSSEAU Pierre-Alain Sallard Hermann Schachner Seth Schoen Gunther Schrack Scott Sherard Alexander Sisson Koen Smidt Guo Song Saul Spatz Stefano Spezia Jonathan Stacey Jakub Staron Nicholas Stearns Ralph Steiner Torsten-Karl Strempel Joshua Swanson David J Sycamore Owain Thomas 3Blue1Brown Nicholas Titterton Emidio Torre Patrick Traill Phat Tran Sheldon Trinder Tutoring uClassify Matthew Unterfenger RWC van den Brink Kiryn van Schalkwyk Alexander Vinnikov Sami Yrjänheikki Lucas Vos Russell Walsmith Debora Weber-Wulff Michael Weiner Woomerang Research Other gifts in 2018: The OEIS Foundation Inc. is extremely grateful to all the editors, all unpaid, who spend so many hours processing submissions and improving OEIS entries. They keep the OEIS up-to-date and accurate. The OEIS Foundation Inc. is also grateful to William Cheswick, Georg Fischer,and others for helping to develop the "OEIS Sequences and Music" exhibit which is to be part of the "La.La.Lab - The Mathematics of Music" exhibition that will open in May 2019 in Heidelberg (Germany). The OEIS Foundation Inc. is also grateful to the American Mathematical Society for facilitating our access to MathSciNet in 2018. Donors in 2017 Gauss Circle Benefactors in 2017 (Gifts of $25000 and above): The Simons Foundation Benefactors in 2017 (Gifts of $5000 and above): Susanna Cuyler and N. J. A. Sloane Sponsors in 2017 (Gifts of $1000 and above): Anonymous David Blair Russ Cox Harvey P. Dale Tom Duff Google and Apple / Benevity Community Impact Fund Fred Kline Donald and Jill Knuth N. J. A. 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In 2016, Russ Cox made a crucial modification to the submissions program, David Applegate set up a defense against the spammers who had been pounding on our site, and David and Russ together handled the migration of the whole OEIS web site to a new platform. These were huge tasks that no one else could have done, and the Foundation is very grateful to them. The OEIS would not survive without all the editorial work carried out by the volunteer editors. There are many who helped in 2016, especially Jean-François Alcover, Joerg Arndt, Alonso Del Arte, Colin Barker, Bruno Berselli, Harvey P. Dale, Michael De Vlieger, Olivier Gérard, Charles Greathouse, G. C. Greubel, Ilya Gutkovskiy, M. F. Hasler, Hans Havermann, Alois P. Heinz, Wesley Ivan Hurt, Sean A. Irvine, Robert Israel, Antti Kartunen, Vaclav Kotesovec, Wolfdieter Lang, Paolo P. Lava, Peter Luschny, Michel Marcus, Omar Pol, Danny Rorabaugh, Jon E. Schoenfield, Michael Somos, David W. Wilson, Robert G. 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OEIS: The Movie To celebrate the launching of the OEIS Foundation, Tony Noe made an 8.5-minute movie showing the first 1000 terms of 1000 sequences, with soundtrack from Recaman's sequence A5132. There are four ways to view the movie: On YouTube (you can always find it by searching for "OEIS Movie"). By downloading a 5 MB QuickTime movie that is viewable with QuickTime Player 7 and some browsers. By downloading a 27 MB movie that uses the H264 codec and AAC sound. This movie is viewable on recent versions of Windows Media Player and most up-to-date browsers. By going to Tony Noe's website for a frame-by-frame display, with links to the OEIS definition of each sequence. (Incidentally, you can convert the movie to just about any other format at http://www.media-convert.com, without downloading any software).

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Email: president(AT)oeisf.org or njasloane(AT)gmail.com. Phone: (732) 828 6098.

