On-Line Encyclopedia of Integer Sequences

OEIS records information on integer sequences of interest to both professional and amateur mathematicians, and is widely cited.

As of February 2024[ref], it contains over 370,000 sequences,[5] and is growing by approximately 30 entries per day.

There is also an advanced search function called SuperSeeker which runs a large number of different algorithms to identify sequences related to the input.

[7] Neil Sloane started collecting integer sequences as a graduate student in 1964 to support his work in combinatorics.

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.

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.

[11] In 2004, Sloane celebrated the addition of the 100,000th sequence to the database, A100000, which counts the marks on the Ishango bone.

[12] 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,[13][14] following a proposal by OEIS Editor-in-Chief Charles Greathouse to choose a special sequence for A200000.

The OEIS was limited to plain ASCII text until 2011, and it still uses a linear form of conventional mathematical notation (such as f(n) for functions, n for running variables, etc.).

Greek letters are usually represented by their full names, e.g., mu for μ, phi for φ.

[18] OEIS normalizes the sequences for lexicographical ordering, (usually) ignoring all initial zeros and ones, and also the sign of each element.

Sequences of weight distribution codes often omit periodically recurring zeros.

[20] In 2009, the OEIS database was used by Philippe Guglielmetti to measure the "importance" of each integer number.

[25] The result shown in the plot on the right shows a clear "gap" between two distinct point clouds,[26] the "uninteresting numbers" (blue dots) and the "interesting" numbers that occur comparatively more often in sequences from the OEIS.

This phenomenon was studied by Nicolas Gauvrit, Jean-Paul Delahaye and Hector Zenil who explained the speed of the two clouds in terms of algorithmic complexity and the gap by social factors based on an artificial preference for sequences of primes, even numbers, geometric and Fibonacci-type sequences and so on.

Second edition of the book
1999 "Integer Sequences" web page
Sloane's "Integer Sequences" web page on the "AT&T research" web site as of 1999
Plot of Sloane's Gap: number of occurrences ( y log scale) of each integer ( x scale) in the OEIS database