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Integer sequence : ウィキペディア英語版 | 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. 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 ''n''th perfect number. == Examples == Integer sequences which have received their own name include: *Abundant numbers *Baum–Sweet sequence *Bell numbers *Binomial coefficients *Carmichael numbers *Catalan numbers *Composite numbers *Deficient numbers *Euler numbers *Even and odd numbers *Factorial numbers *Fibonacci numbers *Fibonacci word *Figurate numbers *Golomb sequence *Happy numbers *Highly totient numbers *Highly composite numbers *Home primes *Hyperperfect numbers *Juggler sequence *Kolakoski sequence *Lucky numbers *Lucas numbers *Padovan numbers *Partition numbers *Perfect numbers *Pseudoperfect numbers *Prime numbers *Pseudoprime numbers *Regular paperfolding sequence *Rudin–Shapiro sequence *Semiperfect numbers *Semiprime numbers *Superperfect numbers *Thue-Morse sequence *Ulam numbers *Weird numbers
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