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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.
The n-Fibonacci constant is the ratio toward which adjacent -Fibonacci numbers tend; it is also called the n th metallic mean, and it is the only positive root of =. For example, the case of n = 1 {\displaystyle n=1} is 1 + 5 2 {\displaystyle {\frac {1+{\sqrt {5}}}{2}}} , or the golden ratio , and the case of n = 2 {\displaystyle n=2} is 1 + 2 ...
In finance, Fibonacci retracement is a method of technical analysis for determining support and resistance levels. [1] It is named after the Fibonacci sequence of numbers, [ 1 ] whose ratios provide price levels to which markets tend to retrace a portion of a move, before a trend continues in the original direction.
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 .
Fibonacci search has an average- and worst-case complexity of O(log n) (see Big O notation). The Fibonacci sequence has the property that a number is the sum of its two predecessors. Therefore the sequence can be computed by repeated addition. The ratio of two consecutive numbers approaches the Golden ratio, 1.618... Binary search works by ...
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]
This analysis fails for p = 2 and p is a divisor of the squarefree part of k 2 + 4, since in these cases are zero divisors, so one must be careful in interpreting 1/2 or +. For p = 2, k 2 + 4 is congruent to 1 mod 2 (for k odd), but the Pisano period is not p − 1 = 1, but rather 3 (in fact, this is also 3 for even k ).
Download as PDF; Printable version; In other projects ... The Fibonacci Association is a mathematical organization that specializes in the Fibonacci number sequence ...