An automatic sequence is a series of numbers that follows a predictable pattern and can be generated by a computer algorithm. This mathematical concept has applications in computer science, cryptography, and other fields.

## Definitions

An automatic sequence is a sequence of numbers that can be generated by a finite automaton. A finite automaton is a mathematical model of a machine that can read a sequence of symbols and change its internal state based on the input. The automaton can be programmed to generate a sequence of numbers based on a set of rules.

## Origin

The concept of automatic sequence was first introduced by the mathematician Axel Thue in 1906. Thue was interested in the properties of sequences of symbols and their relationships to language and cryptography. He discovered that certain sequences could be generated by a finite automaton and that these sequences had interesting mathematical properties.

## Meaning in different dictionaries

The term “automatic sequence” is not commonly found in dictionaries. However, the word “sequence” is defined as a series of numbers or other elements that follow a particular pattern or order. The word “automatic” refers to something that is done without conscious thought or effort.

## Associations

Automatic sequences have applications in computer science, cryptography, and other fields. They are used in the design of computer algorithms, the analysis of data, and the generation of random numbers.

## Synonyms

There are no commonly used synonyms for automatic sequence.

## Antonyms

There are no commonly used antonyms for automatic sequence.

## The same root words

There are no commonly used root words for automatic sequence.

## Example Sentences

- The automatic sequence generated by the computer algorithm was used to encrypt the message.
- The properties of the automatic sequence were analyzed using mathematical techniques.
- The finite automaton was programmed to generate an automatic sequence of numbers.
- The automatic sequence was used to test the performance of the computer algorithm.