Wednesday, 18 July 2012

The On-Line Encyclopedia of Integer Sequences® (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


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