This site is supported by donations to The OEIS Foundation.

# Quotes

## Contents

## Quotations About the OEIS

Over the past fifty years many people have remarked how useful the database has been. These comments have appeared in the achnowledgements sections of articles, or have been sent by email. Here are 150 of these comments (selected from ten thousand citations), arranged by year.

A comment followed by a name and date in square brackets, like this:

"This note could not have been written without the valuable help of the OEIS." [Octavio Alberto Agustín Aquino, 2016]

usually refers to an article listed in the OEIS Wiki pages **Works Citing OEIS**.
Looking up the author's last name in the appropriate section of those pages will provide full details of the source.
If only initials are given, the quotation is usually from an email message.

Comments prior to 1996 refer to the books **A Handbook of Integer Sequences** (1973) or **The Encyclopedia of Integer Sequences** (1995).

Thanks to Michael De Vlieger for relaying many of these quotations.

This page is not yet in its final form. Please send additions or corrections to N. J. A. Sloane (njasloane at gmail dot com).

**Do not make changes here, because they will be lost at the next revision**.

## 1973-1976

"I also found N. J. A. Sloane's A Handbook of Integer Sequences to be an invaluable tool. I shall say no more about this marvelous reference except that every recreational mathematician should buy a copy forthwith" (Martin Gardner, Scientific American, July 1974).

"Incomparable, eccentric, yet very useful. Contains thousands of `well-defined and interesting' infinite integer sequences together with references for each. ... If you ever wondered what comes after 1, 2, 4, 8, 17, 35, 71, ..., this is the place to look it up" (Lynn A. Steen, Amer. Math. Monthly, 1974).

"On comparing the sequence of cardinalities of these sets with a prepublication version of N. J. A. Sloane's handy table [7], we learned what we should have guessed, that anything which nests is often associated with trees....." [R. K. Guy and J. L. Selfridge, 1973]

Other readers said things like "Bought your book and read it cover to cover...," "Bless you for your Handbook of Integer Sequences," "Purchased your indispensable Handbook of Integer Sequences, which is getting a great deal of use, to the detriment of household chores, etc.," "Your book is for sure! Thanks!"

From a geophysicist in Germany: "with great pleasure I read your Handbook of Integer Sequences, which surely is the most comprehensive work in this section of numerical mathematics"

From West Virginia: ``as an astronomer, I have found your book on integer sequences very useful ...;

"I have found your book, A Handbook of Integer Sequences, very useful in my work on generative epistemology."

A graph theorist in Maryland: "... I thought I had something new until your book sent me to the Riordan reference, where I found 80% of my results and so I abandoned the problem."

Harvey J. Hindin, writing from New York City, exuberantly concluded a letter to N. J. A. Sloane by saying: "There's theOld Testament, theNew Testament, and theHandbook of Integer Sequences".

## 1995

"I'm Russian university teacher and system programmer. In school years I subscribed to "Quantum (Kvant)" magazine and in one of articles was founded reference to your 1973-handbook. In student years I order microform of handbook. Its contents serves as "pointing" for my mathematics interests (perfect/amicable numbers, LIFE, polyomino ...). I'm now 5 years on Internet and want to say, that site with SEQUENCE SERVER is _unparalleled_ phenomena on NET. My congratulations and best wishes!" [N.W.M., Nizhny Novgorod, Russia. Apr 25, 1995]

## 1999

"The numbers that came out were 4, 28, 232, 2092, 19864, . . . and we couldn't see a pattern. In desperation, we sent them to superseeker@research.att.com (now superseeker@oeis.org) (a miracle program created by Neil Sloane). ..." [Gilbert Strang, SIAM President, SIAM News, 1999]

## 2001

"The connection between these two appearances would probably not have occurred without Sloane's Handbook of Integer Sequences ..." [E. Deutsch and L. Shapiro, 2001]

## 2005

"For the proof of Lemma 9, the author is indebted to Axel Hultman and Sloane's On-Line Encyclopedia of Integer Sequences." [N. Eriksen, 2005]

## 2006

"Without the OEIS this paper would not exist." [Brad Jackson and Frank Ruskey, 2006]

## 2007

"This paper would have been an impossibility were it not for your database on integer sequences. It gave me many ideas, many of which flourished into theorems." [Angelo B. Mingarelli, 2007]

## 2008

"This paper contains several proofs of identities that we first conjectured on the basis of numerical investigation, hugely facilitated by access to Sloane's wonderful sequence finder." [David H. Bailey et al., 2008]

i love your site and i spend a lots of time on it. This is the best game i have ever found, and it's YOUR creation, YOUR idea. With your database a novice like me can surf into sequences, find new link between numbers. - E.D., Toulouse, France, Mar 3 2008.

## 2010

"Sloane's influential On-Line Encyclopedia of Integer Sequences is an indispensable research tool in the service of the mathematical community..." [A. S. Fraenkel, 2010]

We found that the sums of squares of multinomial coefficients, known to count the number of abelian squares, now have the new interpretation of giving the (2k)-th moment of an n-step random walk in the plane. ... We would also like to thank you for the interesting and crucial role the OEIS played in this research. J.G.W., Mar 28 2010.

## 2011

"Very important to the results in this paper were the search sites KnotInfo by Cha and Livingston [CL11] and The On-Line Encyclopedia of Integer Sequences by Sloane [Slo11]." [Cody Armond and Oliver T. Dasbach, 2011]

## 2012

"The Online Encyclopedia of Integer Sequences [OE] was useful in discovering the formula in part (b)." [D. Dugger, 2012]

Congratulations on your retirement from AT&T. Glad to see that you are continuing your work with the OEIS. It is a marvelous mathematical resource. J.T., Providence, R.I., Feb 26, 2012.

It is an honour to be connected to you. The work you have done for the mathematics community is outstanding. Thank you. R.L., Toronto, Aug 06 2012

Your well-known paper on doubly exponential sequences (with Aho, 1972) got me unstuck on a problem I was working on! I use the OEIS all the time, and so do my students. An incredibly useful research tool. K.D., Nova Scotia, 08/07/2012

[The] impact of [N. J. A. Sloane's] brainchild OEIS (On-line Encyclopedia of Integer Sequences) on today's (and tomorrow's!) mathematical research far surpasses that of any living mathematician. Doron Zeilberger (2012), http://www.math.rutgers.edu/~zeilberg/Opinion124.html

## 2013

It should be noted that the theoretical developments were greatly helped by us first plugging our computational results into the On-Line Encyclopedia of Integer Sequences (OEIS)." [G. Wu and M. G. Parker, 2013]

"It was a knock-out when after entering the sequence 2,5,15,51,187,715,... in the page OEIS, we found a great variety of different interpretations for it..." [Carlos Segovia, 2013]

"Inspired by this connection [with two sequences in the OEIS] we were able to prove the following theorem ..." [H. Mühle, 2013]

I think you have done a fantastic work in initiating and building the oeis. To me it was a life changing event when I discovered the oeis-database online about 6 years ago. - M.G., May 28 2013

I cannot begin to thank you enough for this website, which has led me to many results that I might not have found without the clues and references in the database. It has also shown me much that I thought was original but turned out to be known, but in completely different realms than I was working in. Thanks for that, too! The integers themselves are surely the purest possible common language of so much seemingly disparate work. You've given us an incredible gift here, may it live forever. R.M., Aug 30 2013

P.S. I am only joining an incredibly long queue in saying that your Encyclopedia must be the most valuable public resource in all of Mathematics. J.B.C., Dec 09 2013

A revolutionary mathematical tool appeared online in 1996 — Neil Sloane’s collection of integer sequences, along with mathematical interpretations of the numbers, formulas for generating them, computer code, references, and relevant links. This was the On-Line Encyclopedia of Integer Sequences (OEIS), originally hosted on Sloane’s website at AT&T Labs. Anyone with access to the internet could peruse the database, and anyone could submit a sequence or supplemental data to the database. All for free. Thanks to Sloane’s tireless efforts and a worldwide community of contributors, the collection has grown to well over 200,000 sequences to date, drawing results from all areas of mathematics. Each sequence in the OEIS acts as a fingerprint for an associated theorem. While the fingerprints in the OEIS have a specific input structure, the sequences can arise in many contexts, including arrays of data, coefficients of polynomials, enumeration problems, subway stops, and so on. The OEIS itself is the database for these fingerprints. The impact on research is clearly established by over 3000 articles to date citing the OEIS. Sara C. Billey and Bridget E. Tenner (2013), http://arxiv.org/abs/1304.3866

## 2014

"I'll say a little about how we originally found the main result of this paper in case the reader is curious. ... we calculated ... with the help of computer algebra software, from which we guessed that the coefficients were in fact independent of the vector space. Searching the OEIS then revealed the coefficients probably formed a known sequence, and from there it was not diffcult to prove the main result." [Gunnar Thor Magnússon, 2014]

"As always when confronted with a sequence of integers, it pays off to look at The On-Line Encyclopedia of Integer Sequences http://oeis.org ..." [W. Lanssens et al., 2014]

"the authors also want to thank the On-Line Encyclopedia of Integer Sequences (OEIS) [25] for being a helpful resource in identifying the Bernoulli numbers as coefficients in Eq. (3)." [P. Knechtges et al., 2014]

"The OEIS (2013) was very helpful in identifying the rencontre numbers in some apparently unrelated work, and thus led to the tree construction that is the focus of the present paper." [P. Duchon and R. Duvignau, 2014]

"... those concerned with mathematical heuristics have found that it is useful and makes good sense to create the Online Encyclopedia of Integer Sequences that will attempt to identify a finite sequence from among a large and growing database of sequences that have arisen in theoretical work." [Philip J. Davis, 2014]

The function H(psi) was found by first expanding F in terms of the sum and difference of squares of electric and magnetic charges in a perturbation series. The Taylor coeffcients of the function H(psi) were then recognized as belonging to a hypergeometric series using an algorithm for integer sequence recognition (the OEIS), then simplified in terms of trigonometric functions." [D. D. K. Chow and G. Compère, Black holes in N=8 supergravity ..., 2014]

"... we prove Theorem 2.2 by using the result related with the generating functions of convex compositions given by Andrews [15] and the Online Encyclopedia of Integer Sequences [16] as well as Appell-Lerch sums, we get the desired results." [Bin Chen and Haigang Zhou, 2014]

"After compiling the results of many explicit computations, we noticed that many of the numbers d_{n,r,S} appear in the existing literature in contexts far removed from the enumerative geometry of rank conditions; we owe this surprising (to us) observation to perusal of [Slo14]." [ P. Aluffi, 2014]

I am very pleased to have received a signed copy of your original handbook as an incommensurate reward for A229037. I am still as delighted by the encyclopedia as I was when I first discovered it and I see in it an instructional example both of mathematical beauty and of scientific collaboration. - J.G., Feb 02 2014

Congratulations on the gigantic edifice you have created from that simple beginning. In seeking out your e-mail address I had the opportunity to refresh my understanding of the entire story of the OEIS Foundation -- and it is an astounding tale. It tempts me to replace my badge affiliation of "Retired" with "Old friend of Neil Sloane". I promise not to do so but --- please accept my best wishes and continued life for that once slim volume. It was a good idea at the time and has become a grand idea. - E.F.B., Feb 03 2014

As far as I can guess, most of us are amateurs here. And I think it's one of the nicest features of OEIS, that somebody can add very interesting references and comments on one's sequence many years after it has been submitted.. - K.M., Poland, Feb 05 2014

E.K.'s and my sincere gratitude: The--your--OEIS is awesome for our research in mathematical physics! - M.P., Poland, May 29, 2014

Heartfelt congratulations on the 50th anniversary of the Encyclopedia. This project of yours has been a great inspiration in my work. I consider it one of the great projects in mathematics today, acting as a great unifying force in the field, bringing together an enormous number of investigators, from eminent professionals to amateurs. I wish you also a very pleasant and happy birthday! M.J., Bosnia and Herzegovina, Oct 07 2014

I am very grateful to you for the creation of OEIS. With best wishes, A.C., Riga, University of Latvia, Oct 08 2014

Please find enclosed the link to a paper where I use widely your wonderful database OEIS. - J.-F.C., Toulouse, Oct 08 2024

I am PhD in combinatorics of Nankai University. The project OEIS is wonderful which consists of large amount of materials. - P.B.Z., Oct 10 2014

Allow me to congratulate you on this remarkable anniversary! In my opinion, Mathematics is similar to bionics based on attempts to repeat some perfect properties of plants and animals. Understanding of their perfection is not available to the mankined since such a perfection is based on their deep genetic nature; in mathematics their role is played by sequences, whose often astonishingly deep properties not always are accessible to proofs from modern Mathematics. Therefore, your child OEIS is so important for Mathematics - now and in the future! I wish you many years of health and happiness ! And many-many new successes for You and Your OEIS !! - V.S., Beer-Sheva, Oct 10 2014

I have used the site repeatedly since my high school days and it is one of the greatest pearls in the Internet! F.A., Binghamton, Oct 11 2014

## 2015

"We would like to acknowledge the mathematical software Sage [44] and the Online Encyclopedia of Integer Sequences [33] which were both essential for our investigations." [Laura Florescu et al., 2015]

"I would also like to acknowledge the OEIS and Sage-Combinat (and the entire community developing it); the results in this thesis could not have been obtained without these resources." [Vasu Tewari, 2015]

"There is a Web Page: <https://oeis.org/> by N.J.A. Sloane. It tells, from typing the first few terms of a sequence, whether that sequence has occurred somewhere else in Mathematics. Postgraduate student Daniel Steffen traced this down and found, to our surprise, that the sequence was related to the tangent function tan x. Ryan and Tam searched out what was known about this connection and discovered some apparently new results. We all found this a lot of fun and I hope you will too." [Ross Street, 2015]

"All three authors would like to acknowledge the On-Line Encyclopedia of Integer Sequences [Slo14], without which this project would have been very difficult." [Nicholas Proudfoot, Max Wakefield, and Ben Young, 2015]

"The connection between tensor products of A_oo-maps and hypercubes (Remark 4.2) was discovered by consulting the OEIS." [Matthias Franz, 2015]

"Finally, we thank Sloane for the OEIS [12] which facilitated our making the connection between fence tilings and strongly restricted permutations." [K. Edwards and M. A. Allen, 2015]

"We encounter the amazingly interesting and helpful on-line mathematical tool OEIS ..."" [Karl Dilcher and Larry Ericksen, 2015]

We especially owe a debt of gratitude to Neil Sloane and the OEIS Foundation, Inc. Our work was greatly facilitated by the On-Line Encyclopedia of Integer Sequences." [Sylvie Corteel et al., 2015]

"If it weren't for the OEIS [this work] would not have been possible." [Brad Clardy, 2015]

"Preliminary work using [OEIS] assisted in the identification of the closed formulae in the proposition." [R. Biswal et al., 2015]

... So we send our thanks for all your efforts in creating the OEIS. It has helped us be smarter today than we were yesterday! T.Y., Spring Lake Park Senior High, Jan 04 2015

I am an aspiring academic and have devoted much of my study to combinatorics in cryptography, number theory, and abstract algebra. The OEIS has been a fantastic resource for debugging sequence and matrix generation algorithms. Thank you for ensuring the open-source provision of this powerful mathematical resource. - J.C., Jul 17 2015

The OEIS was absolutely invaluable in this research. We computed the numbers, put them into OEIS, discovered Dean Hickerson's beautiful tatami write-up, put 2+2= 4, did a little work, and got this nice paper published! And now there are 3 grad students at UVic looking at various aspects of Tatami tilings! F.R., Victoria, Oct 04 2015.

A coincidence of sequences which through the OEIS became a theorem: J.-C. Hausmann, Counting polygon spaces, Boolean functions and majority games, arXiv preprint arXiv:1501.07553, 2015

Nicholas Proudfoot, Max Wakefield, and Ben Young, Intersection Cohomology of the Symmetric Reciprocal Plane, Preprint, http://pages.uoregon.edu/njp/ukl-m1.pdf, 2015. ["All three authors would like to acknowledge the On-Line Encyclopedia of Integer Sequences [Slo14], without which this project would have been very difficult."] Dec 21 2015

Margaret Wertheim (2015), Cabinet Magazine, Issue 57, Spring 2015, p. 48: Used widely by professional mathematicians, computer theorists, and scientists, the OEIS has been called the most influential math website in the world. In addition, the database draws a huge international audience of recreational mathematicians, people who, for pleasure, surf its delights to explore the ways in which numbers can play. As a kind of numerological version of the Oxford English Dictionary, the OEIS is the place to go if you want to learn what any sequence of digits might mean, if it has been discovered already, or if it is entirely new.

Manish Gupta (2015), quoted in Nautilus Magazine, Issue 29, Chapter 4: Suppose you are working on a problem in one domain, say, electronics, and while solving a problem you encounter a sequence of integers. Now you can use [the OEIS] and search if this is well known. Many times it happens that this sequence may have appeared in a totally unrelated area with another problem. Since numbers are the computational output of nature, to me, these connections are quite natural.

Eric Egge (2015),Defying God: The Stanley-Wilf Conjecture, Stanley-Wilf Limits, and a Two-Generation Explosion of CombinatoricsinA Century of Advancing Mathematics, M.A.A.: [The] OEIS is a required stop for anyone who encounters an integer sequence they don’t recognize. It’s no exaggeration to observe that in certain parts of combinatorics, the OEIS alone has increased the rate of new discoveries by an order of magnitude.

## 2016

"None of the presented results would have been obtained without the help of the online encyclopedia of integer sequences which gave the crucial hint by recognizing the 3-dimensional Catalan numbers." [Manuel Wettstein, 2016]

"On computing various examples of those using Mathematica and studying the j-th coefficient of a_k(r) as a sequence using the On-Line Encyclopedia of Integer Sequences (OEIS), we made an explicit conjecture for the coefficients of a_k(r) and eventually proved it by quite a different route." [Pieter Moree and SS Eddin, 2016]

"... we have been inspired by the now classical work of Zeilberger on holonomic sequences [19], the PhD thesis and articles of Colton [2], [3], [4] on automated conjecture-making in number theory, and of course the Online Encyclopedia of Integer Sequences (OEIS) [16]. ..." [Andreas Holmstrom, 2016]

"It should be mentioned that all 5 identities in Corollary 6 were first found experimentally by using MAPLE and the OEIS." [Karl Dilcher and Christophe Vignat, 2018]

"We were made aware of OEIS and [28] by an anonymous referee which lead to [27]. An examination of some intger sequences in OEIS reveals that our article provides an alternative explanation for some of the known integer sequences. To our knowledge, the current type of exploration of adjacencies in permutations and their applications are novel." [ Bhadrachalam Chitturi and Krishnaveni K S, 2016]

"OEIS is an amazing instrumental resource, ... a model both for curation and for moderation." [J. M. Borwein, 2016]

"This note could not have been written without the valuable help of the OEIS." [Octavio Alberto Agustín Aquino, 2016]

"Remarkably, this exhaustive enumeration leads us exactly to the integer sequence A001792 of The On-Line Encyclopedia of Integer Sequences... ." [Milica Andelic et al., 2016]

02/24/2016

Manuel Wettstein, Trapezoidal Diagrams, Upward Triangulations, and Prime Catalan Numbers, arXiv:1602.07235 [cs.CG], 2016 and Discr. Comp. Geom. 58 (2017) 505-525. None of the presented results would have been obtained without the help of the online encyclopedia of integer sequences [12], which gave the crucial hint by recognizing the 3-dimensional Catalan numbers. Feb 24 2016

The great thing about the OEIS was that it solved an NP-ish problem for us: once the formula was given to us, it wasn’t that hard to prove that it was correct for our sequence, but finding it in the first place would have been extremely hard without the OEIS. Tim Gowers, Blog, May 10 2016.

11/02/2016

Mario Ziller, John F. Morack Algorithmic concepts for the computation of Jacobsthal's function, arXiv:1611.03310: The authors would like to express their appreciation to the On-Line Encyclopedia of Integer Sequences [17]. It provides an exceptional collection of integer progressions. This data is very informative and helps discover new items and links within the wide field of number theory. Nov 02 2016

"There are numerous research papers and popular scientific notes, video lectures, slides of talks, and web pages (the best way to begin surfing the Web is to visit the On-Line Encyclopedia of Integer Sequences) that are concerned with Farey sequences and their applications." [Andrey O. Matveev, 2017]

## 2017

"The authors are thankful to the On-Line Encyclopedia of Integer Sequences [12], which drew their attention to plane permutations." [Jannik Silvanus and Jens Vygen, 2017]

"On p. 18, note that the OEIS was used to find relevant literature." [Robert A. Proctor and Matthew J. Willis, 2017]

"We would like to thank Neil Sloane’s On-line Encyclopedia of Integer Sequences for directing us to references [4, 7, 21, 28]." [Eric T. Mortenson, 2017]

"Thanks are ... due to all contributors and editors of the websites OEIS.org and PrimePuzzles.net." [Alexei Kourbatov, 2017]

"The Online Encyclopedia of Integer Sequences [Slo16] was invaluable for connecting our data with previously known sequences." [Michael Joseph and Tom Roby. 2017]

"We argue that a database built out of zeta types and Tannakian symbols could lead to interesting discoveries, similar to what has been achieved for example by the OEIS, the LMFDB, and other existing databases of mathematical objects." [Andreas Holmstrom and Torstein Vik, 2017]

"We thank Daniele Dorigoni for identifying this function using The On-Line Encyclopedia of Integer Sequences." [Joseph A. Farrow and Arthur E. Lipstein, 2017]

"Finding a good conjecture [for an integral] relies often on the usage of other Information and Communication Technologies (ICTs), such as online databases, in particular the Online Encyclopedia of Integer Sequences [11]. It provides formulas, references to literature, but also source code for the usage of a CAS. ... Searching these databases is valuable also for cases where the student can compute the integral, as it enables finding new connections with other mathematical fields." [Thierry Dana-Picard and David G. Zeitoun, 2017]

"The On-Line Encyclopedia of Integer Sequences [6] told him that the determinants of these matrices were given by sequence A079340, and a conjectured formula could be found there." [Gaurav Bhatnagar and Christian Krattenthaler, 2017]

"We guessed (2.21) with the help of OEIS ." [Connor Behan, 2017]

"Using the results of these computer searches in the Online Encyclopedia of Integer Sequences, we discovered that this problem, when played on the square grid, is equivalent to several other known problems." [Boris Aronov et al., 2017]

Michael Joseph, Tom Roby, Toggling independent sets of a path graph, arXiv:1701.04956: The Online Encylopedia of Integer Sequences [Slo16] was invaluable for connecting our data with previously known sequences. Jan 18 2017

John D. Wiltshire-Gordon, Alexander Woo, Magdalena Zajaczkowska, Specht Polytopes and Specht Matroids, arXiv:1701.05277. We make the following conjecture with the help of the OEIS [14]... Jan 19 2017

I would like to say thank you for your efforts on OEIS. It is an amazing page. Some time ago we discovered a very unexpected connection between quantum mechanical experiments and graph theory using your OEIS, in particular A000438. We have written an article about it, https://arxiv.org/abs/1705.06646 which has recently accepted in Physical Review Letters (one of the best physics journals). It is hard to overstate the joy at the evening when I started a bunch of calculations investigating a strange property of quantum experiments, and found ... for 4 crystals you get 6240 solutions. Then writing this odd sequence into OEIS, which then gave me exactly one sequence. These few minutes were absolutly amazing, one of the best moment in my scientific career so far. Mario Krenn, University of Vienna, Faculty of Physics. Dec 01, 2017.

## 2018

"We must mention that an invaluable resource while dealing with integer sequences is the Online Encyclopedia of Integer Sequences." [Anandaroop Ray et al., 2018]

"The OEIS database [144] was very helpful." [Martin Klazar, 2018]

"We learned about Lehmer's Theorem 1 via serendipity, thanks to that amazing tool that we are so lucky to have, the On-Line Encyclopedia of Integer Sequences [S] (OEIS). ... the present paper is yet another paper that owes its existence to the OEIS!" [Shalosh B. Ekhad and Doron Zeilberger, 2018]

"We also proved thanks to computer experiments and the OEIS [7] that prographs made of only one sort of operator with two inputs and three outputs can model the biological notion of tandem duplication trees." [Christophe Cordero, 2018]

"Consulting the Online Encyclopedia of Integer Sequences leads us to the work of Labelle in combinatorics; this connection is powerful and unexpected. ... The idea of this lecture is that we begin with “brute force”; then consult the OEIS or some other resource to try to identify our results and find faster/better ways, and to make connections to other works. Then we extract other useful materials from the results, proving what we can." [Eunice Y. S. Chan and Robert M. Corless, 2018]

"Experimental data combined with an OEIS search leads us to the following conjecture...." [Benjamin Braun and Fu Liu, 2018]

"...at least 39 entries in Sloane's OEIS were found containing sequences whose generating functions satisfy Riccati equations, including some entries related to the families of indecomposable combinatorial objects, moments of probability distributions, chord diagrams, Feynman diagrams, etc." [Olivier Bodini et al., 2018]

"This note makes reference to many sequences to be found in the OEIS, which at the time of writing contains more than 300,000 sequences. All who work in the area of integer sequences are profoundly indebted to Neil Sloane. Many of the sequences in this note are related to simplicial objects such as the associahedron and the permutahedron. Indeed, the T-transform provides an enumerative link between these two objects, while the P pipeline brings these two objects back to more basic objects. The comments of Tom Copeland and Peter Bala in the relevant OEIS entries have been very useful in this context." [Paul Barry, 2018]

I wanted to relay a bit of nostalgia and my heartfelt thanks. Back in the late 1990s, I was a high school in Portland, Oregon, USA. While I was interested in mathematics, I had no significant mathematically creative outlet ... until I discovered the OEIS in the course of trying to invent some puzzles for myself. I remember becoming an active contributor through the early 2000s, and eventually at one point, an editor. My experience with the OEIS, and the eventual intervention of one of my high school teachers, catalyzed my interest in studying mathematics, which I eventually did at Reed College. I went on to a Ph.D. in algebraic geomewtry at the University of Pennsylvania, and am currently at Yale. I wanted to thank you for seriously engaging with an 18 year old kid, even though I likely submitted my fair share of mathematically immature sequences. I doubt I would have become a mathematician without the OEIS! Asher Auel, Mar 18 2018

“This continued fraction ought to be classical, but the first mention of which I am aware is a 2006 contribution to the OEIS by Paul D. Hanna, who found it empirically; it was proved a few years later by Josuat-Vergès by a combinatorial method (which also yields a q-generalization).” Alan D. Sokal, The Euler and Springer numbers as moment sequences, arXiv:1804.04498 [math.CO], 2018.

"... Maybe more feasible would be to have some distributed system of open databases, and there are some exemplars out there, in very structured environments. One I like is the NIST digital library of mathematical functions, and another is the On-Line Encyclopedia of Integer Sequences founded by Sloane. There’s potential for doing the same sort of thing with theorems...” David Aldous, A Conversation with Jim Pitman, Statistical Science (2018) Vol. 33, No. 3, 458-467.

"A fantastic source for novel ideas for sequence data is the Online Encyclopedia of Integer Sequences." [Nick Collins, 2019]

Katja Bercic and Janos Vidali, DiscreteZOO: Towards a Fingerprint Database of Discrete Objects, International Congress on Mathematical Software (ICMS 2018): Mathematical Software, Lecture Notes in Computer Science (LNCS) Vol. 10931, 36-44. doi:10.1007/978-3-319-96418-8_5, also arXiv:1812.05921 [math.CO], 2018. "The existence of a natural fingerprint likely played a part in the success of the On-Line Encyclopedia of Integer Sequences (OEIS), perhaps the most famous example of a database of mathematical results. The OEIS is a searchable and collaborative database of integer sequences, which serve as fingerprints for their associated entries. The indexing is based on small, language-independent, and canonical data: the first elements of a sequence."

## 2019

"Our enumerative results establish further connections to the OEIS sequences and some classical combinatorial objects, such as restricted permutations, weighted ordered trees and set partitions. ... The On-Line Encyclopedia of Integer Sequences created by Neil Sloane is very helpful in this research." [Chunyan Yan and Zhicong Lin, 2019]

"JM thanks Karol Penson for introducing to him a wonderful world of the On-Line Encyclopedia of Integer Sequences..." [Aernout van Enter et al., 2019]

"We used the Online Encyclopedia of Integer Sequences to trace related research..." [Luigi Santocanale, 2019]

"We are grateful to the OEIS Foundation Inc. for maintaining an extremely useful online encyclopedia of integer sequences" [Sten A. Reijers, 2019]

The On-Line Encyclopedia of Integer Sequences OEIS is an incredibly valuable tool in mathematical research. As a ‘fingerprint database for theorems’ it allows to identify interconnections and relations between theorems throughout mathematics. In this spirit, FindStat is a collaborative online database of combinatorial statistics on combinatorial collections and of combinatorial maps between such collections." [Martin Rubey and Christian Stump, 2019]

"... we'd like to thank OEIS editors Michel Marcus, Peter Luschny, Jon E. Schoenﬁeld and others for their patient, faithful volunteer work and for useful comments and suggestions during the editing of sequences, concerned with this manuscript." [Kolosov Petro. 2019]

"Steven R. Finch's incredible labor of love, an encyclopedia of mathematical constants, begins with such basics, then moves on to more elaborate topics. ... It appears astonishing to me that a single individual went through all these topics. His achievement can only be compared to the On-Line Encyclopedia of Integer Sequences." [Osmo Pekonen, 2019]

"How to learn if there is a certain regularity in the sequence? The best way is to go to the Online Encyclopedia of Integer Sequences (https://oeis.org/) initiated by Neil James Alexander Sloane, and ask if it contains our sequence." [Tibor Nagy et al., 2 019]

"Also, there are a number of datasets that are highly related to IQ test questions as well. For instance, the Online Encyclopedia of Integer Sequences (OEIS) contains over a quarter-million ... math sequences." [Yusen Liu et al., 2019]

"We are grateful to A. Schreiber for collaboration on [28] which inspired this project and for finding [the OEIS] based on the first few entries of Table 1." [Luke Lippstreu et al., 2019]

"...the useful database OEIS played a key role in linking the various structures in different areas some, of which will be briefly described ..." [Hwang and Jin, 2019]

"The On-Line Encyclopedia of Integer Sequences (OEIS) is a browsable and searchable online resource launched in 1996 that grew out of N.J.A. Sloane's 1973 book A Handbook of Integer Sequences. Starting in 1994, there are 2,752 references to it in zbMATH. Of these, more than 70% cite OEIS as a whole, while the remaining refer to one or, in about 5% of the cases, several actual entries of the database (with a single reference citing as many as 14 sequences in one case). However, in contrast to the previous example, the references to the online service have quickly [replaced] those to the printed handbook. The easy usability of the OEIS and its powerful search features (which benefit from the rather simple data shape of integer sequences) appear to be a crucial factor here, making it a model for highly findable, accessible, and reusable mathematical data. ..." [Klaus Hulek et al., 2019]

"The OEIS is the oldest mathematical database, and arguably the most influential one." [Katja Berčič, 2019]

"In creating this table, we discovered, by way of the OEIS database, that the generating function for \mu = (5,2) is identical to the generating function for the number of so-called metacyclic p-groups for prime p." [Jonathan Bloom and Nathan McNew, 2019]

"We found the formulas for the coefficients in Proposition 11 thanks to OEIS database." [Stefan Barańczuk, 2019]

"... we acknowledge that the On-line Encyclopedia of Integer Sequences has been of great help in this project." [Per Alexandersson et al., 2019]

“The connection between tensor products of A_-maps and hypercubes (Remark 4.2) was discovered by consulting the OEIS.” Matthias Franz, The cohomology rings of homogeneous spaces, arXiv, Sep 26, 2019.

I just found out about oeis.org and honestly it is the most amazing place on the internet. I used to study math so looking at pretty graphs made me really emotional and then reading the bios of some people who posted the sequences was also emotional and i don't know why the numbers make those fancy graphs sometimes ... I am extremely grateful for your work. J.C., a student and teacher from Spain, Sep 25 2019

You should know the OEIS has played a big role not just in my research but also in my teaching these past years. Students seem to find ideas like recurrences and generating functions more "real" when they can look things up and discover new ideas through the database. It also shows them that mathematics is very much *not* a dead subject. Overall, it's truly a wonderful contribution to the world of mathematics! T. Kyle Petersen, DePaul University, Oct 03, 2019

This work was immeasurably facilitated by the On-Line Encyclopedia of Integer Sequences [16]. I warmly thank Neil Sloane for founding this indispensable resource, and the hundreds of volunteers for helping to maintain and expand it. - Alan D. Sokal A remark on the enumeration of rooted labeled trees arXiv:191014519 Nov, 2019

The On-Line Encyclopedia of Integer Sequences (OEIS) is a browsable and searchable online resource launched in 1996 that grew out of N.J.A. Sloane’s 1973 book A Handbook of Integer Sequences. ... references to the online service have quickly replaced those to the printed handbook. The easy usability of the OEIS and its powerful search features (which benefit from the rather simple data shape of integer sequences) appear to be a crucial factor here, making it a model for highly findable, accessible, and reusable mathematical data. Nevertheless, interoperability remains an issue even for this resource. Currently one can only dream of seamlessly cross-linking the generating functions in the OEIS with respective entries in the DLMF – a service which would open a whole new dimension of opportunities. Klaus Hulek, Fabian Müller, Moritz Schubotz, Olaf Teschke, Mathematical Research Data–An Analysis Through zbMATH References, EMS Newsletter (2019) Vol. 9, Issue 133, 54-57. doi:10.4171/NEWS/113/14

... "Step 2. Get the recursive formulae of A_n and B_n using [the OEIS]. Step 3. Compute the first few terms of A_n and B_n and using WolframAlpha and OEIS to guess a closed-form of them." [Zhentao Lu, 2019]

## 2020

"... some surprising connections found over recent years between certain natural subsystems of lambda calculus and the study of graphs on surfaces, ... As with so many other such connections, this one owes its existence to the OEIS, ... as an illustration ... I will explain how to give a reformulation of the Four Color Theorem as a simple statement about typing of lambda terms." [Noam Zeilberger, 2020]

"When Erdenberger [6] appeared on the arXiv, John McKay immediately pointed out that this is the list of supersingular primes A002267, the primes that divide the order of the Monster..." [G. K. Sankaran, 2020]

"An established tool for discovering bijections is the Online Encyclopedia of Integer Sequences (OEIS). This is a phenomenal database of sequences where the entrees are refereed, and there are many references to follow. The OEIS is located at http://www.oeis.org." [Marni Mishna, 2020]

"Without using Neil Sloane's OEIS this essay could have been written, but it would only have been half as much fun." [Peter H. N. Luschny, 2020]

"... the appearance of the sequences of genera for a few small values of p in the [OEIS], which included generating functions for them that suggested immediately a nice and simple conjecture for all dimensions ..." [Santiago López de Medrano, 2020]

"... again it reports a case where I discovered a new mathematical result thanks to OEIS. In fact, I think this case might well be the best ever in my experience so far." [D. E. Knuth, 2020]

"Finally, we would like to thank Prof. N.J.A. Sloane in particular since this work would not be possible without OEIS." [Alkan and Aybar, 2020]

## 2021

"At the very least you should try all that are built into the computer algebra systems that you already have, together with all of the web-based tools (…, the Online Encyclopedia of Integer Sequences, …) because that is so easy to do." [David R. Stoutemyer, 2021]

"Something which is rarely mentioned is the value of OEIS as a very comprehensive source of references to mathematical papers--probably the best there is." [Email from a user of the OEIS, Jan 24 2021]

"The contribution you and the OEIS have made to mathematics as a whole is immeasurable and I cannot begin to thank you enough for creating such a brilliantly useful tool." [Email from a user of the OEIS, Mar 19 2021]

" ... I did eventually find a handful of interesting articles and letters. The key to tracking them down, unsurprisingly, was the Online Encyclopedia of Integer Sequences, which more and more seems to function as the Master Index to Mathematics." Brian Hayes, Does having prime neighbors make you more composite?, Bit-Player Article, Nov 04 2021

Neil, thanks for everything you've done since you first published the Handbook in the 1970's! Some of my best work wouldn't have been possible without the incredible resource you created for all of us. - Jim Propp, Jun 29 2021

I am happy to welcome Russ as President and want to take this opportunity to thank every single one of you for all of the amazing work, collaboration, criticism, and wisdom that you bring to the OEIS. The OEIS is no doubt, a world treasure. - W.H., Jun 29 2021

The On-Line Encyclopedia of Integer Sequences (OEIS) is a triumph, residing at the intersection of mathematics and technology, and appealing to specialists and novices alike. It serves not just as an immense repository (to inform authors of data and connections they may have overlooked), but also as a feedback loop (to motivate and drive research into previously unimagined lines of thought).Steven Finch, The On-Line Encyclopedia of Integer Sequences, founded in 1964 by N. J. A. Sloane, A Tribute to John Horton Conway, The Mathematical Intelligencer (2021) Vol. 43, 146–147.

"... we computed the values of b_{mj} in a range and guessed that b_{mj} = ... via an act of OEIS-enabled perspicacity."- Usman Hafeez, Peter Marcus, Kyle Ormsby, and Angélica M. Osorno, Saturated and linear isometric transfer systems for cyclic groups of order p^m q^n, arXiv:2109.08210, Sep 16 2021

"This database [Slo03] can be said to have “colonised the high ground” in mathematics: mathematicians from all sub-disciplines use it." James Harold Davenport, Digital Collections of Examples in Mathematical Sciences, arXiv:2107.12908 [cs.SC], 2021.

## 2022

"Neither this paper nor my PhD thesis would have happened if it weren't for the OEIS." [Christopher Stokes, commenting on Stokes (2022)]

"We encourage anyone pursuing these problems to make good use of the OEIS, as we were frequently (pleasantly) surprised at the myriad connections to other areas of combinatorics." [V. Bardenova et al., 2022]

"I would like to thank you for creating and maintaining the OEIS - as a physics student it has come to my aid many times!" - T.F., Feb 28 2022

"The connection between tensor products of A_oo-maps and hypercubes (Remark 4.2) was discovered by consulting the OEIS." [Matthias Franz, 2015]

## 2023

Siobhan Roberts, "What Number Comes Next? Ask the Encyclopedia of Integer Sequences.", New York Times, May 21, 2023. "... This year the OEIS, which has been praised as `the master index to mathematics' and `a mathematical equivalent to the FBI’s voluminous fingerprint files,' celebrates its 50th anniversary. ... ... Donald Knuth ... has also chanced upon breakthroughs. Working on a new problem, he always searches the OEIS. `It finds my bedfellows,' he said. `The beautiful thing is that you can compute your way into the literature.'..."

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. Includes summary of facts about OEIS.

## 2024

"Modern tables are still important today, particularly in experimental mathematics. Some prominent examples: In the late 18th century, Legendre and Gauss used tables of prime numbers to conjecture the prime number theorem. In the late 1960s Birch and Swinnerton-Dyer used tables of elliptic curve data to formulate the Birch and Swinnerton-Dyer conecture. The Online Encyclopedia of Integer Sequences (OEIS) has helped discover ( or rediscover ) countless mathematical relationships." Terrence Tao, Machine Assisted Proof, AMS Colloquium Lecture I, Jan 3 2024; Youtube: https://www.youtube.com/watch?v=AayZuuDDKP0

"I would like to use my message to thank you INFINITELY for creating this encyclopedia. This is an essential tool for me and all combinatorics. THANK YOU VERY MUCH THANK YOU VERY MUCH THANK YOU VERY MUCH" [J-L. B., Feb 18 2024]

"OEIS solves real-world problems! One time I needed to optimize accesses to a data structure in my code. By trying out a few examples, I found the optimal order of iterations followed a particular number sequence, but I had no idea on how it could be deduced or calculated analytically. I entered the few examples I had into OEIS and found the solution. The solution involves graduate-level combinatorics and there was no way that I could solve it. Thanks Neil Sloane and OEIS." [Discussion about OEIS on Hacker News, Apr 4, 2024: https://news.ycombinator.com/item?id=39925787]

"I suspect this happens more often than anyone realizes. I really want to read or write the sci-fi story where aliens ping our intelligence with some obscure sequence and they think we're geniuses because thanks to the OEIS we're all like Oh, yeah, that's just A260151, numerators of coefficients c(n) in asymptotic expansion of Sum_{m=1..k} sqrt(m) ~ zeta(-1/2) + (2/3)*k^(3/2) + (-1/2)*k^(1/2) + Sum_{n=0..inf} c(n)/k^(2*n+1/2), here's the next 50 terms." [Discussion about OEIS on Hacker News, Apr 4, 2024: https://news.ycombinator.com/item?id=39925787]

"I had a very similar experience—discovering Stirling numbers of the second kind by solving a computer science problem through brute force, then plugging the results into OEIS, then reverse-engineering an elegant solution to the problem. Fantastic resource." [Discussion about OEIS on Hacker News, Apr 4, 2024: https://news.ycombinator.com/item?id=39925787]

The OEIS is owned, maintained and supported by **The OEIS Foundation Inc.** - please give generously!