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A304588
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Length of shortest prefix of the Thue-Morse word (A010060) such that some length-n block appears twice.
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3
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3, 5, 9, 10, 17, 18, 19, 20, 33, 34, 35, 36, 37, 38, 39, 40, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266
(list;
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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lim inf a(n)/n = 5/2 and lim sup a(n)/n = 4.
a(n) is "2-sychronized", which means that there is an automaton that accepts, in parallel, the base-2 expansions of n and a(n). For this sequence an 8-state automaton suffices. - Jeffrey Shallit, Mar 06 2020
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LINKS
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FORMULA
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EXAMPLE
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For n = 3 we have a(3) = 9 because the first 9 symbols of Thue-Morse are 011010011, and 011 is the first length-3 prefix to be repeated in this prefix.
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PROG
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(PARI) See Links section.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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