Computational investigations of non-repetitive sequences

The need for infinite sequences of symbols with no repetitions seems to have arisen frequently. In view of previous findings about non-repetitive sequences, this paper considers the question whether for some positive integer n, there exists an infinite sequence on two symbols with no three adjacent identical blocks of symbols and no two adjacent identical blocks of symbols of length n or greater. The first result obtained is a lower bound of 4 for the value of n. This is followed by the computation of a 5000-term sequence on two symbols with no three adjacent identical blocks of symbols and no two adjacent identical blocks of symbols of length 4 or greater, evidence which suggests the conjecture that 4 is the greatest lower bound for n. A computation is then performed, the result of which suggests that the traditional methods used in studying nonrepetitive sequences may not be practical for use in determining the status of the above conjecture. Some new concepts and questions are then introduced as aids which may prove useful in further study of this conjecture.