Automatic sequence

In <a href="/facts/Mathematics/pxTouaz4">mathematics</a> and <a href="/facts/Theoretical_computer_science/jSkGGuvy">theoretical computer science</a>, an automatic sequence (also called a k-automatic sequence or a k-recognizable sequence when one wants to indicate that the base of the numerals used is k) is an infinite <a href="/facts/Sequence/gV2S4uqp">sequence</a> of terms characterized by a <a href="/facts/Finite_automaton/GMusWd0a">finite automaton</a>. The n-th term of an automatic sequence a(n) is a mapping of the final state reached in a finite automaton accepting the digits of the number n in some fixed <a href="/facts/Radix/J5RGWRJF">base</a> k.
An automatic set is a set of non-negative integers S for which the sequence of values of its characteristic function χS is an automatic sequence; that is, S is k-automatic if χS(n) is k-automatic, where χS(n) = 1 if n 
 
 
 
 ∈
 
 
 {\displaystyle \in }
 
 S and 0 otherwise.

Automatic sequence open-in-new

Automatic sequence