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Van der Waerden's theorem tells us there can be no infinite binary word avoiding a monochromatic arithmetic progression of length 5 (the longest is of length 177; see A121894). However, Stewart's choral sequence has the property that it has no ababa appearing in arithmetic progression, for a different from b. - Jeffrey Shallit, Jul 03 2020
Van der Waerden's theorem tells us there can be no infinite binary word avoiding a monochromatic arithmetic progression of length 5 (the longest is of length 177; see A121894). However, Stewart's choral sequence has the property that it has no ababa appearing in arithmetic progression, for a different from b. _- _Jeffrey Shallit_, Jul 03 2020
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Van der Waerden's theorem tells us there can be no infinite binary word avoiding a monochromatic arithmetic progression of length 5 (the longest is of length 177; see A121894). However, Stewart's choral sequence has the property that it has no ababa appearing in arithmetic progression, for a different from b. Jeffrey Shallit, Jul 03 2020
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F. M. Dekking, <a href="https://arxiv.org/abs/2001.08915">Permutations of N generated by left-right filling algorithms</a>, arXiv:2001.08915 [math.CO], 2020.
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The sequence is cubefree, i.e., it contains no substrings of the form XXX where X is a sequence of 0s 0's and 1s1's.
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