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Fibonacci sequence. In mathematics, the Fibonacci sequence is a sequence in which each number is the sum of the two preceding ones. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted Fn . The sequence commonly starts from 0 and 1, although some authors start the sequence from 1 and 1 or sometimes ...
In mathematics, a series is, roughly speaking, the operation of adding infinitely many quantities, one after the other, to a given starting quantity. [1] The study of series is a major part of calculus and its generalization, mathematical analysis. Series are used in most areas of mathematics, even for studying finite structures (such as in ...
List of mathematical series. This list of mathematical series contains formulae for finite and infinite sums. It can be used in conjunction with other tools for evaluating sums. is a Bernoulli polynomial. is an Euler number. is the Riemann zeta function. is the gamma function. is a polygamma function. is a polylogarithm.
A number that has the same number of digits as the number of digits in its prime factorization, including exponents but excluding exponents equal to 1. A046758: Extravagant numbers: 4, 6, 8, 9, 12, 18, 20, 22, 24, 26, 28, 30, 33, 34, 36, 38, ... A number that has fewer digits than the number of digits in its prime factorization (including ...
A simple formula is. for positive integer , where is the floor function, which rounds down to the nearest integer. By Wilson's theorem, is prime if and only if . Thus, when is prime, the first factor in the product becomes one, and the formula produces the prime number . But when is not prime, the first factor becomes zero and the formula ...
The Bell number counts the different ways to partition a set that has exactly elements, or equivalently, the equivalence relations on it. also counts the different rhyme schemes for -line poems. [1] As well as appearing in counting problems, these numbers have a different interpretation, as moments of probability distributions.
Pell number. In mathematics, the Pell numbers are an infinite sequence of integers, known since ancient times, that comprise the denominators of the closest rational approximations to the square root of 2. This sequence of approximations begins 1 1, 3 2, 7 5, 17 12, and 41 29, so the sequence of Pell numbers begins with 1, 2, 5, 12, and 29.
Definition and overview. The aliquot sequence starting with a positive integer k can be defined formally in terms of the sum-of-divisors function σ1 or the aliquot sum function s in the following way: [1] If the sn-1 = 0 condition is added, then the terms after 0 are all 0, and all aliquot sequences would be infinite, and we can conjecture ...
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