Online Encyclopedia
Integer sequence
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 n^{2} − 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 a_{n}, 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. There set of all integer sequences is uncountable; thus, almost all integer sequences are incomputable and cannot be defined.
See also
External links
- Journal of Integer Sequences http://www.math.uwaterloo.ca/JIS/index.html . Articles are freely available online.
Topics in mathematics related to quantity |