Infinite 0-1-sequences without long adjacent identical blocks

Abstract. This paper deals with sequences a_1 a_2 a_3 ... of symbols 0 and 1 with the property that they contain no arbitrary long blocks of the form a_{i+1} ... a_{i+k} = ww. The behaviour of this class of sequences with respect to some operations is examined. Especially, the following is shown: Let be a_i^{(0)}=a_i, a_i^{(n+1)}=1/i \sum_{k=1}^i a_k^{(n)}, then there exists a sequence without arbitrary long adjacent identical blocks such that no \lim_{k\to\infty} a_k^{(n)} exists. Let be \alpha \in (0,1), then there exists such a sequence with \lim_{k\to\infty}a_k^{(1)} = \alpha. Furthermore a class of sequences appearing in computer graphics is considered.
helmut@gauss.cam.wits.ac.za,

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