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A217437
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Number of strings of length n in {2,3}* for which at least one of tail(2 S) > tail(S) and tail(3 S) > tail(S) holds.
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0
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2, 1, 2, 1, 5, 3, 12, 9, 19, 16, 38, 20, 59, 42, 104, 65, 213, 111, 400, 245, 765, 439, 1563, 820, 3046, 1731, 5955, 3292, 12078, 6343, 23841, 13090, 47204, 25534, 95140, 50154
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OFFSET
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1,1
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COMMENTS
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The "curling number" k = k(S) of a string of numbers S = s(1), ..., s(m) is defined as follows. Write S as XY^k for strings X and Y (where Y has positive length) and k is maximized, i.e. k = the maximal number of repeating blocks at the end of S.
The "tail length" tail(S) of S is defined as follows: start with S and repeatedly append the curling number (recomputing it at each step) until a 1 is reached; tail(S) is the number of terms that are appended to S before a 1 is reached.
No example is known where both tail(2 S) > tail(S) and tail(3 S) > tail(S) hold.
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LINKS
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EXAMPLE
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Tail(22322)=2, tail(222322)=8, tail(322322)=2, so 22322 is counted in a(5).
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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