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On-Line Encyclopedia of Integer Sequences

Online database of integer sequences

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  • 7 chapters

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OEIS records information on integer sequences of interest to both professional and amateur mathematicians, and is widely cited. As of November 2025, it contains over 390,000 sequences, and is growing by approximately 30 entries per day.

Each entry contains the leading terms of the sequence, keywords, mathematical motivations, literature links, and more, including the option to generate a graph or play a musical representation of the sequence. The database is searchable by keyword, by subsequence, or by any of 16 fields. There is also an advanced search function called SuperSeeker which runs a large number of different algorithms to identify sequences related to the input.

History

Neil Sloane started collecting integer sequences as a graduate student in 1964 to support his work in combinatorics. The database was at first stored on punched cards. He published selections from the database in book form twice:

  1. A Handbook of Integer Sequences (1973, ISBN 0-12-648550-X), containing 2,372 sequences in lexicographic order and assigned numbers from 1 to 2372.
  2. The Encyclopedia of Integer Sequences with Simon Plouffe (1995, ISBN 0-12-558630-2), containing 5,488 sequences and assigned M-numbers from M0000 to M5487. The Encyclopedia includes the references to the corresponding sequences (which may differ in their few initial terms) in A Handbook of Integer Sequences as N-numbers from N0001 to N2372 (instead of 1 to 2372.) The Encyclopedia includes the A-numbers that are used in the OEIS, whereas the Handbook did not.

These books were well-received and, especially after the second publication, mathematicians supplied Sloane with a steady flow of new sequences. The collection became unmanageable in book form, and when the database reached 16,000 entries Sloane decided to go online – first as an email service (August 1994), and soon thereafter as a website (1996). As a spin-off from the database work, Sloane founded the Journal of Integer Sequences in 1998. The database continues to grow at a rate of some 10,000 entries a year. Sloane has personally managed 'his' sequences for almost 40 years, but starting in 2002, a board of associate editors and volunteers has helped maintain the omnibus database. In 2004, Sloane celebrated the addition of the 100,000th sequence to the database, A100000, which counts the marks on the Ishango bone. In 2006, the user interface was overhauled and more advanced search capabilities were added. In 2010 an OEIS wiki was created to simplify the collaboration of the OEIS editors and contributors. The 200,000th sequence, A200000, was added to the database in November 2011; it was initially entered as A200715, and moved to A200000 after a week of discussion on the SeqFan mailing list, following a proposal by OEIS Editor-in-Chief Charles Greathouse to choose a special sequence for A200000. A300000 was defined in February 2018, and by 2026 the database contained more than 390,000 sequences.

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