Holy mole! The last writeup on this node is almost 12 years old! A lot has happened since.
The On-Line Encyclopedia of Integer Sequences is an online database of (have you guessed it?) sequences of Integers (the set of numbers commonly denoted by ℤ) founded by Neil Sloane.1
The encyclopedia began in 1964. Sloane was working on his dissertation, when he came across a certain sequence (1, 8, 78, 944…)2 and was looking for a formula to derive the n-th number in the sequence. His research at the Cornell University library led him to similar sequences, though not the exact one he was looking for. Since smartphones weren’t around then, Sloane recorded these sequences in file cards sorted lexicographically.
The file cards were eventually transferred to punched cards and, in 1967, to a book with 2,372 sequences.3
In 1969 Sloane started working at AT&T Bell Laboratories and over the course of the next 21 years accumulated «a cubic meter of correspondence»4 with praise, further suggestions and updates to the sequences of the book.
In 1995, with the help of Simon Plouffe, the Encyclopedia of Integer Sequences was published5 with 5,487 sequences printed on 587 pages. Amazing! But it wouldn’t stop there.
Once more, Sloane received numerous correspondence from people around the world. This time the collection nearly doubled in size in a year, so in 1996 the magnificent On-Line Encyclopedia of Integer Sequences was born, hosted at the AT&T servers.
However, the entries just kept coming. Between 1996 and 2009 the database grew by more than 10,000 sequences per year. There was also the problem that only Sloane had access to the database and so it was increasingly difficult to maintain the database. In 2002 a group of associate editors started helping but it wasn’t enough. Another big leap had to be done.
On October 27, 2009 Sloane transferred all of his intellectual property and hosting to the OEIS Foundation Inc.6 The original url7 now resolves to the error code 503 Service Unavailable. Now, the OEIS can be reached at https://oeis.org/
Last modified May 8 20:41 EDT 2017. Contains 286111 sequences.
More than sequences
The OEIS hosts more than just a database of sequences. A complete entry at the OEIS has:
- Sequence of integers
- y'know, the actual sequence of numbers
- Offset
- Value and index of the first members of the sequence
- Comments
- An English version of the sequence, in case the title is unreadable. Sometimes these are also unintelligible without knowledge of advanced mathematics, but at least are human-readable. Related sequences also go here.
- References
- Papers or books where the sequence is described and/or used
- Links
- Out-links to the big blue wet internet
- Formula
- When there is one, a mathematical way of generating the numbers
- Example
- Mathematica
- Code for displaying the sequence in Wolfram’s Mathematica
- Prog
- Code for generating the sequence in some programming language
- Keywords
- One or more specific keywords describing properties of the sequence.
- Author
- Extensions
- More credits for people who have extended, corrected or edited by someone else.
More! More!
Also at the OEIS:
Even More!
- Interesting sequences
- Interesting people
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From Wikipedia: Neil James Alexander Sloane (born October 10, 1939) is a British-American mathematician. His major contributions are in the fields of combinatorics, error-correcting codes, and sphere packing. ↩
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Now formalized in the OEIS as A000435: “Normalized total height of all nodes in all rooted trees with n labeled nodes. http://oeis.org/A000435↩
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N. J. A. (1973). A handbook of integer sequences. New York: Academic Press. ISBN 978-0-12-648550-9.↩
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https://oeis.org/wiki/Welcome↩
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Sloane, N. J. A. (1995). The encyclopedia of integer sequences. San Diego: Academic Press. ISBN 0-12-558630-2.↩
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http://oeisf.org/index.html#IPXFER↩
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http://www.research.att.com/~njas/sequences/ol.html↩