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  2. List of integer sequences - Wikipedia

    en.wikipedia.org/wiki/List_of_integer_sequences

    1, 1, 2, 2, 4, 2, 6, 4, 6, 4, ... φ(n) is the number of positive integers not greater than n that are coprime with n. A000010: Lucas numbers L(n) 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, ... L(n) = L(n − 1) + L(n − 2) for n ≥ 2, with L(0) = 2 and L(1) = 1. A000032: Prime numbers p n: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, ... The prime numbers p ...

  3. Arithmetic progression - Wikipedia

    en.wikipedia.org/wiki/Arithmetic_progression

    For instance, the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with a common difference of 2. If the initial term of an arithmetic progression is a 1 {\displaystyle a_{1}} and the common difference of successive members is d {\displaystyle d} , then the n {\displaystyle n} -th term of the sequence ( a n {\displaystyle a_{n ...

  4. 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.

  5. Look-and-say sequence - Wikipedia

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

    This variation ultimately ends up repeating the number 21322314 ("two 1s, three 2s, two 3s and one 4"). These sequences differ in several notable ways from the look-and-say sequence. Notably, unlike the Conway sequences, a given term of the pea pattern does not uniquely define the preceding term.

  6. Mathematics - Wikipedia

    en.wikipedia.org/wiki/Mathematics

    With the large number of new areas of mathematics that have appeared since the beginning of the 20th century, defining mathematics by its object of study has become increasingly difficult. [174] For example, in lieu of a definition, Saunders Mac Lane in Mathematics, form and function summarizes the basics of several areas of mathematics ...

  7. 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.

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