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  2. List of integer sequences - Wikipedia

    en.wikipedia.org/wiki/List_of_integer_sequences

    Magic numbers: 2, 8, 20, 28, 50, 82, 126, ... A number of nucleons (either protons or neutrons) such that they are arranged into complete shells within the atomic nucleus. A018226: Superperfect numbers: 2, 4, 16, 64, 4096, 65536, 262144, 1073741824, 1152921504606846976, 309485009821345068724781056, ... Positive integers n for which σ 2 (n ...

  3. Padovan sequence - Wikipedia

    en.wikipedia.org/wiki/Padovan_sequence

    P(n) is the number of ways of writing n + 2 as an ordered sum in which each term is either 2 or 3 (i.e. the number of compositions of n + 2 in which each term is either 2 or 3). For example, P(6) = 4, and there are 4 ways to write 8 as an ordered sum of 2s and 3s: 2 + 2 + 2 + 2 ; 2 + 3 + 3 ; 3 + 2 + 3 ; 3 + 3 + 2

  4. Look-and-say sequence - Wikipedia

    en.wikipedia.org/wiki/Look-and-say_sequence

    The look-and-say sequence is also popularly known as the Morris Number Sequence, after cryptographer Robert Morris, and the puzzle "What is the next number in the sequence 1, 11, 21, 1211, 111221?" is sometimes referred to as the Cuckoo's Egg , from a description of Morris in Clifford Stoll 's book The Cuckoo's Egg .

  5. Fibonacci sequence - Wikipedia

    en.wikipedia.org/wiki/Fibonacci_sequence

    Lucas numbers have L 1 = 1, L 2 = 3, and L n = L n−1 + L n−2. Primefree sequences use the Fibonacci recursion with other starting points to generate sequences in which all numbers are composite. Letting a number be a linear function (other than the sum) of the 2 preceding numbers. The Pell numbers have P n = 2P n−1 + P n−2.

  6. Pell number - Wikipedia

    en.wikipedia.org/wiki/Pell_number

    In words: the first two numbers in the sequence are both 2, and each successive number is formed by adding twice the previous Pell–Lucas number to the Pell–Lucas number before that, or equivalently, by adding the next Pell number to the previous Pell number: thus, 82 is the companion to 29, and 82 = 2 × 34 + 14 = 70 + 12.

  7. Lucas number - Wikipedia

    en.wikipedia.org/wiki/Lucas_number

    The sequence also has a variety of relationships with the Fibonacci numbers, like the fact that adding any two Fibonacci numbers two terms apart in the Fibonacci sequence results in the Lucas number in between. [3] The first few Lucas numbers are 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364, 2207, 3571, 5778, 9349, ... .

  8. Integer sequence - Wikipedia

    en.wikipedia.org/wiki/Integer_sequence

    An integer sequence is computable if there exists an algorithm that, given n, calculates a n, for all n > 0. The set of computable integer sequences is countable.The set of all integer sequences is uncountable (with cardinality equal to that of the continuum), and so not all integer sequences are computable.

  9. Recamán's sequence - Wikipedia

    en.wikipedia.org/wiki/Recamán's_sequence

    In mathematics and computer science, Recamán's sequence [1] [2] is a well known sequence defined by a recurrence relation. Because its elements are related to the previous elements in a straightforward way, they are often defined using recursion .

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