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  2. Fibonacci sequence - Wikipedia

    en.wikipedia.org/wiki/Fibonacci_sequence

    All these sequences may be viewed as generalizations of the Fibonacci sequence. In particular, Binet's formula may be generalized to any sequence that is a solution of a homogeneous linear difference equation with constant coefficients. Some specific examples that are close, in some sense, to the Fibonacci sequence include:

  3. Wall–Sun–Sun prime - Wikipedia

    en.wikipedia.org/wiki/Wall–Sun–Sun_prime

    The k-Wall–Sun–Sun primes can be explicitly defined as primes p such that p 2 divides the k-Fibonacci number (()), where F k (n) = U n (k, −1) is a Lucas sequence of the first kind with discriminant D = k 2 + 4 and () is the Pisano period of k-Fibonacci numbers modulo p. [15]

  4. Generalizations of Fibonacci numbers - Wikipedia

    en.wikipedia.org/wiki/Generalizations_of...

    A repfigit, or Keith number, is an integer such that, when its digits start a Fibonacci sequence with that number of digits, the original number is eventually reached. An example is 47, because the Fibonacci sequence starting with 4 and 7 (4, 7, 11, 18, 29, 47) reaches 47. A repfigit can be a tribonacci sequence if there are 3 digits in the ...

  5. List of types of numbers - Wikipedia

    en.wikipedia.org/wiki/List_of_types_of_numbers

    Computable number: A real number whose digits can be computed by some algorithm. Period: A number which can be computed as the integral of some algebraic function over an algebraic domain. Definable number: A real number that can be defined uniquely using a first-order formula with one free variable in the language of set theory.

  6. Fibonacci numbers in popular culture - Wikipedia

    en.wikipedia.org/wiki/Fibonacci_numbers_in...

    These numbers are calculated from using the Fibonacci sequence in some way to reveal patterns in both natural and artificial systems, essentially allowing the characters to predict the future. In the CBS show Numb3rs episode "Thirteen", a Fibonacci sequence is embedded in a numeric code left behind by a serial killer.

  7. Fibonacci - Wikipedia

    en.wikipedia.org/wiki/Fibonacci

    In the Fibonacci sequence, each number is the sum of the previous two numbers. Fibonacci omitted the "0" and first "1" included today and began the sequence with 1, 2, 3, ... . He carried the calculation up to the thirteenth place, the value 233, though another manuscript carries it to the next place, the value 377.

  8. 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:

  9. Liber Abaci - Wikipedia

    en.wikipedia.org/wiki/Liber_Abaci

    Another example in this chapter involves the growth of a population of rabbits, where the solution requires generating a numerical sequence. [8] Although the problem dates back long before Leonardo, its inclusion in his book is why the Fibonacci sequence is named after him today.