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 nth 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 nth term: an explicit definition.
Alternatively, an integer sequence may be defined by a property which members of the sequence possess and other integers do not possess. For example, we can determine whether a given integer is a perfect number, even though we do not have a formula for the nth perfect number.
Read more about Integer Sequence: Examples, Computable and Definable Sequences, Complete Sequences
Famous quotes containing the word sequence:
“We have defined a story as a narrative of events arranged in their time-sequence. A plot is also a narrative of events, the emphasis falling on causality. “The king died and then the queen died” is a story. “The king died, and then the queen died of grief” is a plot. The time sequence is preserved, but the sense of causality overshadows it.”
—E.M. (Edward Morgan)