A Pseudorandom number sequence is a sequence of numbers that has been computed by some defined arithmetic process but is effectively a random number sequence for the purpose for which it is required.
Although a pseudorandom number sequence in this sense often appears to lack any definite pattern, any pseudorandom number generator with a finite internal state will repeat after a very long sequence of numbers. This can be proved using the pigeonhole principle.
See also: Pseudorandom number generator.