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Integer Sequence

An integer sequence is a sequence whose terms are integers. The most complete printed references for such sequences are Sloane (1973) and its update, Sloane and Plouffe (1995). The sequences from both works are included in the vastly expanded On-Line Encyclopedia of Integer Sequences, founded by Neil Sloane (2003) and maintained by The OEIS Foundation Inc. (https://oeis.org/). In this listing, sequences are identified by a unique 6-digit A-number. Sequences appearing in Sloane and Plouffe (1995) are ordered lexicographically and identified with a 4-digit M-number, and those appearing in Sloane (1973) are identified with a 4-digit N-number. To look up sequences, use the OEIS web interface at https://oeis.org/.

Integer sequences can be analyzed by a variety of techniques (Sloane and Plouffe 1995, p. 26), including the application of a data compression algorithm (Bell et al. 1990), computation of the discrete Fourier transform (Loxton 1989), or searching for a linear recurrence equation connecting the terms or a generating function producing them. There are also a large number of transformations which relate integer sequences to one another, including the Euler transform, exponential transform, Möbius transform, and others (Bower, Sloane).

Candidate closed-form solutions fitting supplied terms of an integer sequence can be sought in the Wolfram Language using FindSequenceFunction[seq]. Agreement with a finite list of terms does not establish the formula for the entire sequence.

In the Season 2 episode "Backscatter" (2006) of the television crime drama NUMB3RS, math genius Charlie Eppes poses a problem of identifying an integer sequence to his students, one of whom uses Sloane's Online Encyclopedia of Integer Sequences to find it.

See also

Combinatorics, Consecutive Number Sequences, Generating Function, Integer Sequence Primes, Linear Recurrence Equation, Möbius Transform, Number, Padovan Sequence, Sequence, Smarandache Sequences

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References

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Integer Sequence

Cite this as:

Weisstein, Eric W. "Integer Sequence." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/IntegerSequence.html

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