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A059129
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A hierarchical sequence (W2{2}* - see A059126).
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3
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1, 2, 1, 2, 3, 2, 1, 2, 1, 3, 4, 3, 1, 2, 1, 2, 3, 2, 1, 2, 1, 4, 5, 4, 1, 2, 1, 2, 3, 2, 1, 2, 1, 3, 4, 3, 1, 2, 1, 2, 3, 2, 1, 2, 1, 5, 6, 5, 1, 2, 1, 2, 3, 2, 1, 2, 1, 3, 4, 3, 1, 2, 1, 2, 3, 2, 1, 2, 1, 4, 5, 4, 1, 2, 1, 2, 3, 2, 1, 2, 1, 3, 4, 3, 1, 2, 1, 2, 3, 2, 1, 2, 1, 6, 7, 6, 1, 2, 1, 2, 3, 2, 1, 2, 1
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OFFSET
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0,2
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COMMENTS
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Begin with the empty finite sequence s_0. Inductively extend s_n to obtain s_{n+1} as follows: if s_n is given by a, b, c, ..., d, e, f, with g being the least integer that is not a value of s_n, then s_{n+1} is a, b, c, ..., d, e, f, g, -f, -e, -d, ..., -c, -d, -a, -g. The terms of {a(n)} give the absolute values of the limit of these sequences. These finite sequences naturally describe elements of fundamental groups occurring in picture-hanging puzzles and Brunnian links. - Thomas Anton, Oct 15 2022
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LINKS
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E. D. Demaine, M. L. Demaine, Y. N. Minsky, J. S. B. Mitchell, R. L. Rivest, and M. Patrascu, Picture-Hanging Puzzles, arXiv:1203.3602, [cs.DS], 2012-2014.
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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