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Integer sequence - Definition and Overview |
| Related Words: Afterlife, Aftermath, Arrangement, Array, Articulation, Bank, Buzz, Catena, Catenation, Chain, Chasing, Classification, Concatenation, Connection, Consequence, Consequent, Consistency, Continuity, Continuum |
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In mathematics, an integer sequence is a sequence (i.e., an ordered list) of integers.
An integer sequence may be specified explicitly by giving a formula for its n-th term, or implicitly by giving a relationship between its terms. For example, the sequence 0, 1, 1, 2, 3, 5, 8, 13, ... (the Fibonacci sequence) is formed by starting with 0 and 1 and then adding any two consecutive terms to obtain the next one: an implicit description. The sequence 0, 3, 8, 15, ... is formed according to the formula n2 − 1 for the n-th term: an explicit definition.
Integer sequences which have received their own name include:
An integer sequence is a computable sequence, if there exists an algorithm which given n, calculates an, for all n > 0. An integer sequence is a definable sequence, if there exists some statement P(x) which is true for that integer sequence x and false for all other integer sequences. The set of computable integer sequences and definable integer sequences are both countable, with the computable sequences a proper subset of the definable sequences. The set of all integer sequences is uncountable; thus, almost all integer sequences are uncomputable and cannot be defined.
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Example Usage of sequence |
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vehandojo: One sequence of #NewMoon that I like was when the wolves were chasing Victoria, and that only works because of the wonderful song. |
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filipecarvalho: Cool insight into House's title sequence in an article on Fast Company http://www.paulmatthaeus.com/articles/FastCompany.pdf |
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cyclingamericas: There is a real buzz from filming a cracking sequence. Sometimes you know straight away that something will be in the documentary. |
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