目录 一 Welcome to The On-Line Encyclopedia of Integer Sequences® (OEIS®) Wiki 二 Some Famous Sequences 三 General Information About OEIS 四 Introductory chapters from the 1973 and 1995 books; Supplement 3 to 1973 book 五 Description of OEIS entries (or, What is the Next Term?) 六 OEIS: Brief History 七 OEIS: The Movie 八 Arrangement of the Sequences in Database 九 Format Used in Replies From the Database 十 指数 十一 Sequences Which Agree For a Long Time 十二 Recent Additions 十三 Compressed Versions 十四 Contributing a New Sequence, Comment or More Terms 十五 OEIS Search Bar 十六 Email Addresses, Getting in Touch With Authors 十七 Ombudsman 十八 Sequences in Classic Books 十九 Citations 二十 Referencing the OEIS 二十一 URLs 二十二 Referencing a Particular Sequence 二十三 Acknowledgments 二十四 Like us on Facebook! 二十五 Links to Other Sites 二十六 OEIS Mentioned in WolframAlpha Timeline 二十七 Awards and press clippings 二十八 Copyright Notice
Welcome to The On-Line Encyclopedia of Integer Sequences® (OEIS®) Wiki
Some Famous Sequences Recamán's sequence, A005132 The Busy Beaver problem, A060843 The Catalan numbers, A000108 The prime numbers, A000040 The Mersenne primes, A000043 和 A000668 The Fibonacci numbers, A000045
General Information About OEIS Most people use the OEIS to get information about a particular number sequence. If you are a new visitor, then you might ask the database if it can recognize your favorite sequence, if you have one. To do this, go to the main look-up page , enter the sequence, and click 搜索 。 You could also look for your sequence in the <b>指数</b> 。 You might also look at the demonstration pages to see more examples of how to use the OEIS. If your favorite sequence isn't in the database, and if it is interesting, please submit it using the web page for Contributing a new sequence or comment 。 Of course the sequence should be well-defined, of general interest and ideally it should be infinite. Short sequences such as phone numbers are not appropriate. Before submitting a new sequence, you must first 注册 。 If you have stumped the database, you can try Superseeker , which tries really hard to identify a sequence. Send an empty email message to email@example.com to get instructions. You can browse the database, using the WebCam 。 This can be set to look at the most interesting sequences, recent additions, or sequences needing more terms. It can be quite addictive! It is also interesting to browse the <b>指数</b> to the OEIS to see the variety of topics that are covered. In a way the OEIS can be regarded as an index to all of science. It is like a dictionary or fingerprint file for number sequences. You might also like to see the <b>list of papers that have acknowledged help from the database</b> and some comments from readers 。
Introductory chapters from the 1973 and 1995 books; Supplement 3 to 1973 book
Description of OEIS entries (or, What is the Next Term?) The main table in the OEIS is a collection of over a quarter-million number sequences. The entry for each sequence gives some or all of: the beginning of the sequence its name or description a graph of the sequence additional comments the offset (index of first term) references or links formulas computer programs cross-references to other sequences the sequence converted to music the name of the person who submitted it the history of the OEIS entry
For further information about the format of replies received from the database, 点击这里 。 See also the hints file for further useful information. The sequence pages have little buttons at the top marked " 列表 ", " 图表 ", " refs ", " 听 ", " 历史 ", " 文本 ", " internal format ", and sometimes " 表 " and " 编辑 ". " list " produces a numbered list of the terms, plus a bracketed list suitable for importing into other programs such as Maple, Mathemtica, PARI, etc. " refs " shows all the sequences which reference this one. " 表 ": If the sequence is formed by reading a triangle across rows (or by reading a table by antidiagonals), this button produces three different two-dimensional views of the sequence. For an example, see Pascal's triangle, A007318 。 " 图表 " produces two plots of the sequence. The first is a pin plot of the first 200 terms (less if fewer terms are available), the second is a linear or log scatter-plot of all available terms, using terms from the b-file if there is one. Some noteworthy plots are the Fibonacci numbers A000045 , the partition numbers A000041 , the Euler phi-function A000010 , etc. " 听 " produces a midi file so that you can listen to the sequence. The first time you use it you will probably have to tell your browser to allow popups from the OEIS web site. Try listening to Recaman's sequence A005132 , turn the volume up to 127 and set the instrument to #103 ! " history " shows the history of changes to this entry. " 编辑 " (you will see this only if you are a registered user) enables you to propose changes to the sequence. " text " shows the various sections of the entry for this sequence with each line prefixed by a symbol that indicates its function. " Internal format " shows the various sections of the entry for this sequence in the internal format.
OEIS: Brief History
OEIS: The Movie 打开（放） YouTube (you can find it by searching for "OEIS" and "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 definitions of the sequences.
Arrangement of the Sequences in Database Sequences in the OEIS are arranged in lexicographic order , indexed by the position of the first term that is greater than 1 in absolute value. Sequences that contain only 0's, 1's and -1's are in lexicographic order by absolute value at the beginning of the table. Thus there is an essentially unique place to look in order to see if a sequence is already in the table. (If it isn't, submit it and it will probably be added if it is sufficiently interesting - see contributing a new sequence or comment .) Each entry in the OEIS has a link called Sequence in context , which shows the three sequences immediately before and after it in the lexicographic order. (If you don't see it, click on the A-number.) There is also a link called Adjacent sequences , which shows the three entries whose A-numbers are immediately before and after the current sequence. These two links can be very useful when you are looking for a sequence in the OEIS but you are not sure of some of the terms.
Format Used in Replies From the Database
指数 There is an <b>指数</b> to the most important sequences. 这个 main look-up page will also allow you to search for a word (or do much more complicated searches) in the database.
Sequences Which Agree For a Long Time People are always asking about this, so there is a section about them in the <b>指数</b> 。
Recent Additions Recent additions to the OEIS can be seen by clicking the Recent Additions 链接 You can also browse the recent additions using the WebCam 。
Compressed Versions There is a gzipped file containing just the sequences and their A-numbers (a few tens of megabytes) There is also a gzipped file containing just the names of the sequences and their A-numbers (a few megabytes)
Contributing a New Sequence, Comment or More Terms For contributing a new sequence, comment or more terms for an existing sequence, see this page 。 Want to help? See also the page future projects (this page needs updating)
OEIS Search Bar
Email Addresses, Getting in Touch With Authors
Sequences in Classic Books L. Comtet's Advanced Combinatorics R. L. Graham, D. E. Knuth and O. Patashnik's Concrete Mathematics F. Harary and E. M. Palmer's Graphical Enumeration R. P. Stanley's 计数组合学 。
Citations The lists of Works Citing the Encyclopedia of Integer Sequences show some of the ways that people have used the database.
Referencing the OEIS
URLs The URL for the main lookup page is https://oeis.org The URL for the present page is https://oeis.org/wiki/Welcome
Referencing a Particular Sequence If you are writing a paper and wish to refer the Catalan numbers, say (sequence A000108 ), but don't want to digress to describe them, simply add a reference or link that points directly to that sequence in the OEIS. A text reference might say: In an HTML file one might say something like this: ... where the C(n) are the Catalan numbers (<a href="http://oeis.org/ A000108 ">Sequence A000108 </a> in [OEIS]).
Acknowledgments A very large number of people have contributed to the database, and it would be impossible to thank them individually. Special thanks to Antti Karttunen , who wrote the program that displays sequences based on arrays (those with keyword "tabl") in three different two-dimensional formats. To see this, look at some of the following sequences, and click on the keyword "tabl":
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Links to Other Sites
b-file Maple programs written by R. J. Mathar
Caldwell's Prime Pages
Combinatorial Object Server (originally by Frank Ruskey)
Davalan's Jeux et Mathématiques
De Geest's World of Numbers
Encyclopedia of Combinatorial Structures
数学常量 by Steven R. Finch
Journal of Integer Sequences
The Nth Prime Page
Plouffe's Inverter (see also the Inverse Symbolic Calculator )
SeqFan Mailing List
Primo (primality proving program)
Neil Sloane's home page
Eric Weisstein's MathWorld
OEIS Mentioned in WolframAlpha Timeline The OEIS appears (under 1973) in WolframAlpha's Timeline of Systematic Data and the Development of Computable Knowledge , which extends from cave paintings to the present day.
Awards and press clippings The TV series Mr Robot mentioned the OEIS in Season 2, Episode 11 or 12 (there are conflicting reports), September 2016, about 37 minutes in. They are deciphering a cryptic message with the aid of the OEIS. The scene lasts for two to three minutes (which is a lot of screen time). The Dutch magazine Pythagoras has an ongoing series of articles about number sequences, many of which mention the OEIS. Four parts have appeared so far: Een Lexicon vol Getallen ["A Dictionary of Numbers"] (Sept. 2015), Getallenplantjes ["Number plants" (?) ] (Oct. 2015), Driehoeksgetallen ["Triangular numbers"] (Nov. 2015), Een bizarre rij [A bizarre sequence] (Dec. 2015). Margaret Wertheim, The Fax Numbers of the Beast, and Other Mathematical Sports: An Interview with Neil Sloane ， Cabinet Magazine , Issue 57, Spring 2015, pages 48-54. Siobhan Roberts, How to Build a Search Engine for Mathematics: The surprising power of Neil Sloane's Encyclopedia of Integer Sequences , Nautilus Magazine, Issue 29, Chapter 4, Oct 22 2015. Eric Egge in Defying God: The Stanley-Wilf Conjecture, Stanley-Wilf Limits, and a Two-Generation Explosion of Combinatorics , pp. 65-82 of A Century of Advancing Mathematic , ed. S. F. Kennedy et al., MAA Press 2015, says: "When we enter our terms 1, 2, 6; 22, 91, 408, 1938, 9614 into the OEIS search box, we are rewarded with a description of the sequence .... In hindsight it’s amusing that Sloane called his  book “A Handbook,” as though there might be competitors. There are none, and 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." Featured by Slashdot on August 7 2015 Erica Klarreich, The Connoisseur of Number Sequences , Quanta Magazine, August 6 2015 (Interview with Neil Sloane about the OEIS)
黑客新闻 discussion of OEIS, July 21 2015
Article by Vijayakumar Ambat in Malayalam (a regional language of India) in the newspaper Malayala Manorama - Padhippura, 12 June 2015, that mentions the OEIS.
视频访谈 about the OEIS by Marc Chamberland made at the Joint Math Meetings in San Antoio, Texas, Jan. 2015. Alex Bellos, Neil Sloane: the man who loved only integer sequences , Alexs-adventures-in-numberland blog, The Guardian, Oct 07 2014.