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In mathematics and computer science, Recamán's sequence [1] [2] is a well known sequence defined by a recurrence relation. Because its elements are related to the previous elements in a straightforward way, they are often defined using recursion.
Here, the composite number 90 is made up of one atom of the prime number 2, two atoms of the prime number 3, and one atom of the prime number 5. This fact can be used to find the lcm of a set of numbers. Example: lcm(8,9,21) Factor each number and express it as a product of prime number powers.
In computer science, corecursion is a type of operation that is dual to recursion.Whereas recursion works analytically, starting on data further from a base case and breaking it down into smaller data and repeating until one reaches a base case, corecursion works synthetically, starting from a base case and building it up, iteratively producing data further removed from a base case.
The Carmichael lambda function of a prime power can be expressed in terms of the Euler totient. Any number that is not 1 or a prime power can be written uniquely as the product of distinct prime powers, in which case λ of the product is the least common multiple of the λ of the prime power factors.
A primitive recursive set function is a function from sets to sets that can be obtained from the following basic functions by repeatedly applying the following rules of substitution and recursion: The basic functions are: Projection: P n,m (x 1, ..., x n) = x m for 0 ≤ m ≤ n; Zero: F(x) = 0
In computability theory, a primitive recursive function is, roughly speaking, a function that can be computed by a computer program whose loops are all "for" loops (that is, an upper bound of the number of iterations of every loop is fixed before entering the loop).
s −1 = 0, t −1 = 1. Using this recursion, Bézout's integers s and t are given by s = s N and t = t N, where N + 1 is the step on which the algorithm terminates with r N+1 = 0. The validity of this approach can be shown by induction. Assume that the recursion formula is correct up to step k − 1 of the algorithm; in other words, assume ...
In functional programming, fold (also termed reduce, accumulate, aggregate, compress, or inject) refers to a family of higher-order functions that analyze a recursive data structure and through use of a given combining operation, recombine the results of recursively processing its constituent parts, building up a return value.