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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 ...
The look-and-say sequence is also popularly known as the Morris Number Sequence, after cryptographer Robert Morris, and the puzzle "What is the next number in the sequence 1, 11, 21, 1211, 111221?" is sometimes referred to as the Cuckoo's Egg , from a description of Morris in Clifford Stoll 's book The Cuckoo's Egg .
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 ...
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.
Multiplication table from 1 to 10 drawn to scale with the upper-right half labeled with prime factorisations. In mathematics, a multiplication table (sometimes, less formally, a times table) is a mathematical table used to define a multiplication operation for an algebraic system.
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.