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To encode an integer N: . Find the largest Fibonacci number equal to or less than N; subtract this number from N, keeping track of the remainder.; If the number subtracted was the i th Fibonacci number F(i), put a 1 in place i − 2 in the code word (counting the left most digit as place 0).
Fibonacci numbers are used in a polyphase version of the merge sort algorithm in which an unsorted list is divided into two lists whose lengths correspond to sequential Fibonacci numbers—by dividing the list so that the two parts have lengths in the approximate proportion φ.
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.
Pages in category "Fibonacci numbers" The following 48 pages are in this category, out of 48 total. This list may not reflect recent changes. ...
For generalized Fibonacci sequences (satisfying the same recurrence relation, but with other initial values, e.g. the Lucas numbers) the number of occurrences of 0 per cycle is 0, 1, 2, or 4. The ratio of the Pisano period of n and the number of zeros modulo n in the cycle gives the rank of apparition or Fibonacci entry point of n .
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 ...
The Fibonacci numbers are the best known concept named after Leonardo of Pisa, known as Fibonacci. Among others are the following. Among others are the following. Concepts in mathematics and computing
A prime divides if and only if p is congruent to ±1 modulo 5, and p divides + if and only if it is congruent to ±2 modulo 5. (For p = 5, F 5 = 5 so 5 divides F 5) . Fibonacci numbers that have a prime index p do not share any common divisors greater than 1 with the preceding Fibonacci numbers, due to the identity: [6]