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A sequence number is a consecutive number in a sequence of numbers, usually of real integers (natural numbers).Sequence numbers have many practical applications. They can be used, among other things, as part of serial numbers on manufactured parts, in case management, [1] or in databases as a surrogate key for registering and identifying unique entries in a table [2] [3] (in which case it is ...
An integer sequence is computable if there exists an algorithm that, given n, calculates a n, for all n > 0. The set of computable integer sequences is countable.The set of all integer sequences is uncountable (with cardinality equal to that of the continuum), and so not all integer sequences are computable.
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 sequence of six consecutive nines occurs in the decimal representation of the number pi (π), starting at the 762nd decimal place. [ 1 ] [ 2 ] It has become famous because of the mathematical coincidence , and because of the idea that one could memorize the digits of π up to that point, and then suggest that π is rational .
There are a number of ways to denote a sequence, some of which are more useful for specific types of sequences. One way to specify a sequence is to list all its elements. For example, the first four odd numbers form the sequence (1, 3, 5, 7). This notation is used for infinite sequences as well.
In number theory, primes in arithmetic progression are any sequence of at least three prime numbers that are consecutive terms in an arithmetic progression. An example is the sequence of primes (3, 7, 11), which is given by a n = 3 + 4 n {\displaystyle a_{n}=3+4n} for 0 ≤ n ≤ 2 {\displaystyle 0\leq n\leq 2} .
A pronic number is a number that is the product of two consecutive integers, that is, a number of the form (+). [1] The study of these numbers dates back to Aristotle.They are also called oblong numbers, heteromecic numbers, [2] or rectangular numbers; [3] however, the term "rectangular number" has also been applied to the composite numbers.
In number theory, a polite number is a positive integer that can be written as the sum of two or more consecutive positive integers. A positive integer which is not polite is called impolite. [1] [2] The impolite numbers are exactly the powers of two, and the polite numbers are the natural numbers that are not powers of two.