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Automated theorem proving. Automated theorem proving (also known as ATP or automated deduction) is a subfield of automated reasoning and mathematical logic dealing with proving mathematical theorems by computer programs. Automated reasoning over mathematical proof was a major motivating factor for the development of computer science.
φ(n) is the number of positive integers not greater than n that are coprime with n. A000010. Lucas numbers L(n) 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, ... L(n) = L(n − 1) + L(n − 2) for n ≥ 2, with L(0) = 2 and L(1) = 1. A000032. Prime numbers pn. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, ... The prime numbers pn, with n ≥ 1.
For instance, the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with a common difference of 2. If the initial term of an arithmetic progression is a 1 {\displaystyle a_{1}} and the common difference of successive members is d {\displaystyle d} , then the n {\displaystyle n} -th term of the sequence ( a n {\displaystyle a_{n ...
Definition. [] As with the Fibonacci numbers, each Lucas number is defined to be the sum of its two immediately previous terms, thereby forming a Fibonacci integer sequence. The first two Lucas numbers are and , which differs from the first two Fibonacci numbers and . Though closely related in definition, Lucas and Fibonacci numbers exhibit ...
Sequence. An infinite sequence of real numbers (in blue). This sequence is neither increasing, decreasing, convergent, nor Cauchy. It is, however, bounded. In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
In mathematics and computer programming, the order of operations is a collection of rules that reflect conventions about which operations to perform first in order to evaluate a given mathematical expression. These rules are formalized with a ranking of the operations. The rank of an operation is called its precedence, and an operation with a ...
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.
Subsequence. In mathematics, a subsequence of a given sequence is a sequence that can be derived from the given sequence by deleting some or no elements without changing the order of the remaining elements. For example, the sequence is a subsequence of obtained after removal of elements and The relation of one sequence being the subsequence of ...