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  2. Sequence - Wikipedia

    en.wikipedia.org/wiki/Sequence

    An infinite sequence of real numbers (in blue). This sequence is neither increasing, decreasing, convergent, nor Cauchy. It is, however, bounded. In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called elements, or terms).

  3. List of integer sequences - Wikipedia

    en.wikipedia.org/wiki/List_of_integer_sequences

    Recamán's sequence: 0, 1, 3, 6, 2, 7, 13, 20, 12, 21, 11, 22, 10, 23, 9, 24, 8, 25, 43, 62, ... "subtract if possible, otherwise add": a(0) = 0; for n > 0, a(n) = a(n − 1) − n if that number is positive and not already in the sequence, otherwise a(n) = a(n − 1) + n, whether or not that number is already in the sequence. A005132: Look-and ...

  4. Fibonacci sequence - Wikipedia

    en.wikipedia.org/wiki/Fibonacci_sequence

    In mathematics, the Fibonacci sequence is a sequence in which each number is the sum of the two ... The Fibonacci numbers are also an example of a complete sequence ...

  5. Absolutely and completely monotonic functions and sequences

    en.wikipedia.org/wiki/Absolutely_and_completely...

    The notions of completely and absolutely monotone function/sequence play an important role in several areas of mathematics. For example, in classical analysis they occur in the proof of the positivity of integrals involving Bessel functions or the positivity of Cesàro means of certain Jacobi series. [ 6 ]

  6. List of mathematical series - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_series

    This list of mathematical series contains formulae for finite and infinite sums. It can be used in conjunction with other tools for evaluating sums. Here, is taken to have the value

  7. Complete sequence - Wikipedia

    en.wikipedia.org/wiki/Complete_sequence

    For example, the sequence of powers of two (1, 2, 4, 8, ...), the basis of the binary numeral system, is a complete sequence; given any natural number, we can choose the values corresponding to the 1 bits in its binary representation and sum them to obtain that number (e.g. 37 = 100101 2 = 1 + 4 + 32). This sequence is minimal, since no value ...

  8. Integer sequence - Wikipedia

    en.wikipedia.org/wiki/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.

  9. Oscillation (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Oscillation_(mathematics)

    Oscillation of a sequence (shown in blue) is the difference between the limit superior and limit inferior of the sequence. In mathematics, the oscillation of a function or a sequence is a number that quantifies how much that sequence or function varies between its extreme values as it approaches infinity or a point.

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