Recurrent word

In mathematics, a recurrent word or sequence is an infinite word over a finite alphabet in which every factor occurs infinitely many times. An infinite word is recurrent if and only if it is a sesquipower.
A uniformly recurrent word is a recurrent word in which for any given factor "X" in the sequence, there is some length "n""X" (often much longer than the length of "X") such that "X" appears in "every" block of length "n""X". The terms minimal sequence and almost periodic sequence (Muchnik, Semenov, Ushakov 2003) are also used.