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Gilbreath's conjecture is a conjecture in number theory regarding the sequences generated by applying the forward difference operator to consecutive prime numbers and leaving the results unsigned, and then repeating this process on consecutive terms in the resulting sequence, and so forth.
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 ...
Moreover, every positive integer can be written in a unique way as the sum of one or more distinct Fibonacci numbers in such a way that the sum does not include any two consecutive Fibonacci numbers. This is known as Zeckendorf's theorem , and a sum of Fibonacci numbers that satisfies these conditions is called a Zeckendorf representation.
Beginning of the Fibonacci sequence on a building in Gothenburg. In mathematics, an integer sequence is a sequence (i.e., an ordered list) of integers.. An integer sequence may be specified explicitly by giving a formula for its nth term, or implicitly by giving a relationship between its terms.
The exponential distribution, which describes the time between consecutive rare random events in a process with no memory. The exponential-logarithmic distribution The F-distribution , which is the distribution of the ratio of two (normalized) chi-squared-distributed random variables, used in the analysis of variance .
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
Consecutive primes in arithmetic progression refers to at least three consecutive primes which are consecutive terms in an arithmetic progression. Note that unlike an AP-k, all the other numbers between the terms of the progression must be composite. For example, the AP-3 {3, 7, 11} does not qualify, because 5 is also a prime.
The palindromic density of the infinite Fibonacci word is thus 1/φ, where φ is the golden ratio: this is the largest possible value for aperiodic words. [3] In the infinite Fibonacci word, the ratio (number of letters)/(number of zeroes) is φ, as is the ratio of zeroes to ones. [4]