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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. Each code word ends with "11" and contains no other instances of "11" before the end.
The actual values are only computed when needed. For example, one could create a function that creates an infinite list (often called a stream) of Fibonacci numbers. The calculation of the n-th Fibonacci number would be merely the extraction of that element from the infinite list, forcing the evaluation of only the first n members of the list.
An example of a Python generator returning an iterator for the Fibonacci numbers using Python's yield statement follows: def fibonacci ( limit ): a , b = 0 , 1 for _ in range ( limit ): yield a a , b = b , a + b for number in fibonacci ( 100 ): # The generator constructs an iterator print ( number )
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 ...
The number in the n-th month is the n-th Fibonacci number. [21] The name "Fibonacci sequence" was first used by the 19th-century number theorist Édouard Lucas. [22] Solution to Fibonacci rabbit problem: In a growing idealized population, the number of rabbit pairs form the Fibonacci sequence.
When eager evaluation is desirable (primarily when the sequence is finite, as otherwise evaluation will never terminate), one can either convert to a list, or use a parallel construction that creates a list instead of a generator. For example, in Python a generator g can be evaluated to a list l via l = list(g), while in F# the sequence ...
The smallest integer m > 1 such that p n # + m is a prime number, where the primorial p n # is the product of the first n prime numbers. A005235 Semiperfect numbers
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.