|
|
|
|
|
Integer SequenceIn 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. See also External links
|
 |
|
| Copyright 2005-2009 OnPedia.com. All Rights Reserved |
|
|