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:

1. To own the intellectual property known as “The On-Line Encyclopedia of Integer Sequences®” (or “OEIS®”).
2. To maintain the OEIS as a service that is freely accessible by the general public.
3. To act so as to maintain its own existence indefinitely.
4. 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 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.)

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.

Announcement. June 28 2021: Russ Cox is new President of OEIS Foundation, Neil Sloane is now Chairman.

At a meeting of the Trustees of The OEIS Foundation Inc. on June 27 2021 it was decided that Russ Cox will take over as President of the Foundation and Neil Sloane will become Chairman of the Board.

The main reason for this change is that Neil is now 81, and wishes to spend more time on his writing projects (which naturally involve sequences).

The OEIS Foundation Inc. was set up in 2009 as a 501(c)(3) Public Charity whose purpose is to own, maintain and raise funds to support The On-Line Encyclopedia of Integer Sequences (or OEIS) database. Neil James Alexander Sloane served as President of the Foundation from its creation until the present. Russell Stensby Cox has been a Trustee of the Foundation since its creation and has been Vice-President since 2019.

But Russ’s association with the OEIS goes back a lot longer than that. He has been a contributor to and supporter of the database for more than 25 years. He was of great help when the OEIS was still on Neil Sloane’s home page at AT&T Bell Labs, and since the OEIS was moved to an independent hosting service in 2009/2010, Russ has been in charge of the software. Russ’s programs are the reason our server responds so quickly to the 630,000 queries we get every day.

The OEIS could not be in better hands.

[The On-Line Encyclopedia of Integer Sequences, or OEIS (https://oeis.org) was started in 1964 and has been online since 1995. It provides a unique service to the scientific community, identifying number sequences and providing comprehensive information about them. It contains 345,000 entries, has 10,000 registered users, and has been cited in the scientific literature nearly 10,000 times, very often with a comment that “this result would not have been discovered without the help of the OEIS”.]

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.

Change of Registered Agent. July 7 2021: The Registered Agent for the OEIS Foundation Inc is now The CT Corporation System, 829 Bear Tavern Rd, West Trenton, NJ 08628. See the Certificate.

Tax-exempt status in New Jersey

On November 3, 2009 we filed documents with various agencies of the State of New Jersey to register the OEIS Foundation Inc. as a new charity in NJ, and to apply for exemption from NJ business tax and NJ sales and use tax.
On November 12, 2009 we received a letter of exemption from NJ business tax.
On November 24, 2009 we received a letter of exemption from NJ sales and use tax.
On November 24, 2009 we also received a NJ Sales Tax Exempt Organization Certificate.
On December 2, 2009 we received a NJ New Charities Registration letter.

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.

The “Continuing Use” certification of the Trademark “OEIS” was accepted by the United States Patent and Trademark Office on February 20, 2021. This means that the Trademark “OEIS”, Registration No. 3916748, has been renewed for ten years. me are very grateful to Merck & Co., Inc., and in particular Kelly Ann Panno and Lisa Jakob of the Merck Office of General Counsel, working “Pro Bono”, who submitted these certifications on behalf of the OEIS Foundation. We also thank Christine Michelle Duffy oand Kate Marchese ef 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.)

Financial reports

The annual financial reports for the Foundation will be posted on this web site each Spring.

The Treasurer’s Reports for 2010, 2011, 2012, and 2013 were corrected and certified on December 28 2018 by Mark Pollachek, President, Westminster Tax Services.

Treasurer’s Report for 2009 IRS Form 990-N for 2009

Treasurer’s Report for 2010 IRS Form 990-N for 2010

Treasurer’s Report for 2011 IRS Form 990-N for 2011

Treasurer’s Report for 2012 IRS Form 990-N for 2012

Treasurer’s Report for 2013 IRS Form 990-N for 2013

Treasurer’s Report for 2014 IRS Form 990-N for 2014

Treasurer’s Report for 2015 IRS Form 990-N for 2015.

Treasurer’s Report for 2016 IRS Form 990-N for 2016.

Treasurer’s Report for 2017 IRS Form 990-EZ for 2017.

Treasurer’s Report for 2018 IRS Form 990-EZ for 2018, 990-EZ(A) for 2018.

Treasurer’s Report for 2019 IRS Form 990-EZ for 2019, IRS Form 990-EZ(A) for 2019.

Treasurer’s Report for 2020 IRS Form 990-EZ for 2020, IRS Form 990-SA for 2020.

Treasurer’s Report for 2021 IRS Form 990-EZ for 2021.

Treasurer’s Report for 2022 IRS Form 990-EZ for 2022.

Treasurer’s Report for 2023 IRS Form 990-EZ for 2023.

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. As of March 2023, the Fundraising Committee consists of Russ Cox (Chair, OEIS Foundation President), Neil Sloane (OEIS Foundation Chair), Marc LeBrun (OEIS Foundation Vice President), Harvey P. Dale (OEIS Foundation Trustee), and William Cheswick (Advisor).

The OEIS posters

There are now three posters. They may be downloaded without charge, and make excellent wall decorations.

• OEIS.org 2014 (11" x 17"). A new poster, illustrating nine recent sequences (out of a quarter of a million); created by Neil J. A. Sloane in December 2014.
• Small version of 2014 poster (8.5" x 11").
• Postcard version of 2014 poster (4 x 4.5").
• Key to 2014 poster (8.5" x 11")
• Blue poster for The OEIS Foundation Inc. (11" x 17"). This is the second version, created by Lucas Garron (then at Stanford University) in May 2010.
• The original Poster for The OEIS Foundation Inc. (11" x 17"). This is the first version, created by David Applegate and Neil J. A. Sloane in September 2009. It is still our favorite.
• Small version of the original poster. (8.5" x 11")
• Key to the original poster (8.5" x 11")

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:

1. On YouTube (you can always find it by searching for “OEIS Movie”).
2. By downloading a 5 MB QuickTime movie that is viewable with QuickTime Player 7 and some browsers.
3. 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.
4. 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).

To contact the OEIS Foundation.

For financial matters, direct contributions, donations, please contact:

Robert Roy Price,
Treasurer, The OEIS Foundation Inc.,
2340 Saunders Station Road,
Monroeville, PA 15146, USA
Email address: treasurer(AT)oeisf.org

For anything else, please contact:

Russ Cox,
President,
The OEIS Foundation Inc.,
Email: president(AT)oeisf.org