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A292092
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Consider Watanabe's 3-shift tag system {00/1011} applied to the word (100)^n; a(n) = length of first word we see that is in the cycle, if the orbit cycles, or 0 if the orbit reaches the empty string, or -1 if the orbit is unbounded.
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7
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56, 56, 16, 56, 0, 28, 38, 42, 0, 34, 0, 34, 34, 82, 20, 0, 70, 100, 20, 0, 20, 0, 0, 56, 0, 46, 64, 64, 64, 92, 74, 34, 118, 66, 88, 52, 0, 0, 34, 268, 42, 34, 0, 46, 30, 92, 0, 16, 34, 76, 76, 34, 34, 38, 110, 20, 64, 92, 46, 56, 0, 46, 76, 0, 74, 0, 88, 0
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OFFSET
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1,1
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COMMENTS
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Watanabe's tag system {00/1011} maps a word w over {0,1} to w', where if w begins with 0, w' is obtained by appending 00 to w and deleting the first three letters, or if w begins with 1, w' is obtained by appending 1011 to w and deleting the first three letters.
The empty word is included in the count.
Following Asveld we set a(n)=0 if the orbit ends at the empty word.
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LINKS
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Shigeru Watanabe, Periodicity of Post's normal process of tag, in Jerome Fox, ed., Proceedings of Symposium on Mathematical Theory of Automata, New York, April 1962, Polytechnic Press, Polytechnic Institute of Brooklyn, 1963, pp. 83-99. [Annotated scanned copy]
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EXAMPLE
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The following is the analog of columns 3 through 7 of Asveld's Table 1.
1 [171, 6, 56, 59, 138]
2 [166, 6, 56, 59, 133]
3 [11, 6, 16, 17, 10]
4 [154, 6, 56, 59, 121]
5 [105, 0, 0, 31, 24]
6 [14, 518, 28, 85, 215]
7 [57, 6, 38, 41, 36]
8 [68, 518, 42, 85, 333]
9 [173, 0, 0, 49, 38]
10 [1098, 6, 34, 159, 407]
11 [8265, 0, 0, 328, 4429]
12 [720, 6, 34, 93, 343]
13 [1715, 6, 34, 93, 1338]
14 [130, 28, 82, 83, 85]
15 [1979, 6, 20, 215, 720]
16 [2024, 0, 0, 193, 1023]
17 [833, 6, 70, 121, 420]
18 [162, 34, 100, 101, 105]
19 [591, 6, 20, 109, 118]
20 [6124, 0, 0, 357, 2259]
21 [59673, 6, 20, 781, 33530]
22 [748, 0, 0, 150, 328]
23 [11631, 0, 0, 273, 6250]
24 [3200, 6, 56, 261, 1515]
...
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CROSSREFS
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Asveld's Table 1 gives data about the behavior of Post's 3-shift tag system {00/1101} applied to the word (100)^n. The first column gives n, the nonzero values in column 2 give A291792, and columns 3 through 7 give A284119, 291793 (or A284121), A291794, A291795, A291796. For the corresponding data for Watanabe's 3-shift tag system {00/1011} applied to (100)^n see A292089, A292090, A292091, A292092, A292093, A292094.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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