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  2. Fibonacci sequence - Wikipedia

    en.wikipedia.org/wiki/Fibonacci_sequence

    In mathematics, the Fibonacci sequence is a sequence in which each element is the sum of the two elements that precede it. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers , commonly denoted F n .

  3. Liber Abaci - Wikipedia

    en.wikipedia.org/wiki/Liber_Abaci

    Fibonacci used a composite fraction notation in which a sequence of numerators and denominators shared the same fraction bar; each such term represented an additional fraction of the given numerator divided by the product of all the denominators below and to the right of it.

  4. Harmonic progression (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Harmonic_progression...

    Equivalently, a sequence is a harmonic progression when each term is the harmonic mean of the neighboring terms. As a third equivalent characterization, it is an infinite sequence of the form 1 a , 1 a + d , 1 a + 2 d , 1 a + 3 d , ⋯ , {\displaystyle {\frac {1}{a}},\ {\frac {1}{a+d}},\ {\frac {1}{a+2d}},\ {\frac {1}{a+3d}},\cdots ,}

  5. Three-term recurrence relation - Wikipedia

    en.wikipedia.org/wiki/Three-term_recurrence_relation

    If the {} and {} are constant and independent of the step index n, then the TTRR is a Linear recurrence with constant coefficients of order 2.Arguably the simplest, and most prominent, example for this case is the Fibonacci sequence, which has constant coefficients = =.

  6. Greedy algorithm for Egyptian fractions - Wikipedia

    en.wikipedia.org/wiki/Greedy_algorithm_for...

    In mathematics, the greedy algorithm for Egyptian fractions is a greedy algorithm, first described by Fibonacci, for transforming rational numbers into Egyptian fractions. An Egyptian fraction is a representation of an irreducible fraction as a sum of distinct unit fractions, such as ⁠ 5 / 6 ⁠ = ⁠ 1 / 2 ⁠ + ⁠ 1 / 3 ⁠.

  7. Pisano period - Wikipedia

    en.wikipedia.org/wiki/Pisano_period

    For any integer n, the sequence of Fibonacci numbers F i taken modulo n is periodic. The Pisano period, denoted π ( n ), is the length of the period of this sequence. For example, the sequence of Fibonacci numbers modulo 3 begins:

  8. Lucas number - Wikipedia

    en.wikipedia.org/wiki/Lucas_number

    The Lucas sequence has the same recursive relationship as the Fibonacci sequence, where each term is the sum of the two previous terms, but with different starting values. [1] This produces a sequence where the ratios of successive terms approach the golden ratio, and in fact the terms themselves are roundings of integer powers of the golden ...

  9. Fibonacci prime - Wikipedia

    en.wikipedia.org/wiki/Fibonacci_prime

    That is to say, the Fibonacci sequence is a divisibility sequence. F p is prime for 8 of the first 10 primes p; the exceptions are F 2 = 1 and F 19 = 4181 = 37 × 113. However, Fibonacci primes appear to become rarer as the index increases. F p is prime for only 26 of the 1229 primes p smaller than 10,000. [3]

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