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A224763
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Define a sequence of rationals by S(1)=1; for n>=1, write S(1),...,S(n) as XY^k, Y nonempty, where the fractional exponent k is maximized, and set S(n+1)=k; sequence gives denominators of S(1), S(2), ...
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2
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1, 1, 1, 1, 2, 1, 2, 1, 5, 1, 4, 1, 2, 3, 1, 3, 2, 4, 7, 1, 5, 12, 1, 3, 4, 7, 7, 1, 5, 4, 5, 2, 15, 1, 6, 1, 2, 5, 7, 13, 1, 5, 4, 13, 1, 4, 3, 23, 1, 4, 2, 14, 1, 4, 2, 4, 1, 4, 2, 4, 1, 53, 1, 6, 29, 1, 3, 20, 1, 3, 3, 1, 3, 3, 1, 14, 24, 1, 6, 15, 1, 3, 9, 1, 3, 3, 4, 29, 1, 5, 24, 14, 16, 1, 5, 5, 1, 3, 13, 1, 3, 3, 16
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OFFSET
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1,5
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COMMENTS
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k is the "fractional curling number" of S(1),...,S(n). The infinite sequence S(1), S(2), ... is a fractional analog of Gijswijt's sequence A090822.
For the first 1000 terms, 1 <= S(n) <= 2. Is this always true?
See A224762 for definition and Maple program.
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LINKS
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EXAMPLE
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The sequence S(1), S(2), ... begins 1, 1, 2, 1, 3/2, 1, 3/2, 2, 6/5, 1, 5/4, 1, 3/2, 4/3, 1, 4/3, 3/2, 5/4, 8/7, 1, 6/5, 13/12, 1, 4/3, 5/4, 8/7, 9/7, 1, 6/5, 5/4, 6/5, 3/2, 16/15, 1, 7/6, 1, 3/2, 6/5, 8/7, 14/13, 1, 6/5, 5/4, 16/13, 1, 5/4, 4/3, 24/23, 1, 5/4, 3/2, 15/14, 1, 5/4, 3/2, 7/4, ...
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MAPLE
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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Conference dinner party, Workshop on Challenges in Combinatorics on Words, Fields Institute, Toronto, Apr 22 2013, entered by N. J. A. Sloane
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STATUS
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approved
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