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  2. 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 ...

  3. Fibonacci sequence - Wikipedia

    en.wikipedia.org/wiki/Fibonacci_sequence

    Fibonacci sequence. In mathematics, the Fibonacci sequence is a sequence in which each number is the sum of the two preceding ones. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted Fn . Many writers begin the sequence with 0 and 1, although some authors start it from 1 and 1 [1][2] and some (as ...

  4. 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

  5. Hofstadter sequence - Wikipedia

    en.wikipedia.org/wiki/Hofstadter_sequence

    The Hofstadter Figure-Figure (R and S) sequences are a pair of complementary integer sequences defined as follows [1][2] ; S 1. {\displaystyle {\begin {aligned}R (1)&=1~;\ S (1)=2\\R (n)&=R (n-1)+S (n-1),\quad n>1.\end {aligned}}} with the sequence defined as a strictly increasing series of positive integers not present in .

  6. Maximum length sequence - Wikipedia

    en.wikipedia.org/wiki/Maximum_length_sequence

    A maximum length sequence (MLS) is a type of pseudorandom binary sequence.. They are bit sequences generated using maximal linear-feedback shift registers and are so called because they are periodic and reproduce every binary sequence (except the zero vector) that can be represented by the shift registers (i.e., for length-m registers they produce a sequence of length 2 m − 1).

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  8. Van der Waerden's theorem - Wikipedia

    en.wikipedia.org/wiki/Van_der_Waerden's_theorem

    Van der Waerden's theorem is a theorem in the branch of mathematics called Ramsey theory.Van der Waerden's theorem states that for any given positive integers r and k, there is some number N such that if the integers {1, 2, ..., N} are colored, each with one of r different colors, then there are at least k integers in arithmetic progression whose elements are of the same color.

  9. Why Milton could become one of the most destructive ...

    www.aol.com/life-threatening-storm-surge-likely...

    The metropolitan area is home to more than 3 million residents. “Milton has the potential to be one of the most destructive hurricanes on record for west-central Florida,” the National ...

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