Integer sequence (nonfiction): Difference between revisions
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[[File:Fibonacci_sequence_on_a_building_in_Gothenburg.jpg|thumb|]]In [[Mathematics (nonfiction)|mathematics]], an '''integer sequence''' is a sequence (i.e., an ordered list) of [[Integer (nonfiction)|integers]]. | [[File:Fibonacci_sequence_on_a_building_in_Gothenburg.jpg|thumb|Fibonacci sequence on a building in Gothenburg.]]In [[Mathematics (nonfiction)|mathematics]], an '''integer sequence''' is a sequence (i.e., an ordered list) of [[Integer (nonfiction)|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. | 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. | ||
Latest revision as of 05:52, 19 April 2019
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.
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External links:
- Integer sequence @ Wikipedia
- On-Line Encyclopedia of Integer Sequences - an online database of integer sequences, also cited as Sloane's after creator Neal Sloane.