Integer Sequence

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An Integer Sequence is a number sequence that is composed of integer numbers.



  • (Wikipedia, 2015) ⇒ Retrieved:2015-4-22.
    • 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.


    • QUOTE: The sequence database was begun by Neil J. A. Sloane (henceforth, "NJAS") in early 1964 when he was a graduate student at Cornell University in Ithaca, NY. He had encountered a sequence of numbers while working on his dissertation, namely 1, 8, 78, 944, … (now entry A000435 in the OEIS), and was looking for a formula for the n-th term, in order to determine the rate of growth of the terms.

      He noticed that although several books in the Cornell library contained sequences somewhat similar to this, this particular sequence was not mentioned. In order to keep track of the sequences in these books, NJAS started recording them on file cards, which he sorted into lexicographic order.

      Here is a scan of the page in NJAS's thesis notebook with the very first collection of sequences.