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Let k be defined as an element in F, the array of Fibonacci numbers. n = F m is the array size. If n is not a Fibonacci number, let F m be the smallest number in F that is greater than n. The array of Fibonacci numbers is defined where F k+2 = F k+1 + F k, when k ≥ 0, F 1 = 1, and F 0 = 1. To test whether an item is in the list of ordered ...
In mathematics and computing, Fibonacci coding is a universal code [citation needed] which encodes positive integers into binary code words. It is one example of representations of integers based on Fibonacci numbers .
The usual Fibonacci numbers are a Fibonacci sequence of order 2. The cases n = 3 {\displaystyle n=3} and n = 4 {\displaystyle n=4} have been thoroughly investigated. The number of compositions of nonnegative integers into parts that are at most n {\displaystyle n} is a Fibonacci sequence of order n {\displaystyle n} .
A recursive Fibonacci algorithm on a 1.8 GHz Intel Centrino laptop with 512 MB RAM yields a noticeable difference in results between Microsoft Visual C++ compiler 13.10.3052 and TCC. To calculate the 49th Fibonacci number, it took a MS Visual C++ program approximately 18% longer than the TCC compiled program. [citation needed]
A Lagged Fibonacci generator (LFG or sometimes LFib) is an example of a pseudorandom number generator. This class of random number generator is aimed at being an improvement on the 'standard' linear congruential generator. These are based on a generalisation of the Fibonacci sequence. The Fibonacci sequence may be described by the recurrence ...
A Fibonacci 31 bit linear feedback shift register with taps at positions 28 and 31, giving it a maximum cycle and period at this speed of nearly 6.7 years. The bit positions that affect the next state are called the taps. In the diagram the taps are [16,14,13,11]. The rightmost bit of the LFSR is called the output bit, which is always also a tap.
In computer science, a Fibonacci heap is a data structure for priority queue operations, consisting of a collection of heap-ordered trees. It has a better amortized running time than many other priority queue data structures including the binary heap and binomial heap .
A Fibonacci prime is a Fibonacci number that is prime. The first few are: [46] 2, 3, 5, 13, 89, 233, 1597, 28657, 514229, ... Fibonacci primes with thousands of digits have been found, but it is not known whether there are infinitely many. [47] F kn is divisible by F n, so, apart from F 4 = 3, any Fibonacci prime must have a prime index.