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A284119
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Preperiod (or threshold) of orbit of Post's {00, 1101} tag system applied to the word (100)^n, or -1 if this word has an unbounded trajectory.
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30
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4, 15, 10, 25, 411, 47, 2128, 853, 372, 2805, 366, 2603, 703, 37912, 612, 127, 998, 2401, 1200, 623, 5280, 1778, 1462, 4346269, 4129, 3241, 7018, 3885, 14632, 7019, 4564, 4277, 147688, 1857, 11120, 81141, 20204, 3847, 116014, 7635, 6488, 5665, 6142, 73515, 5826, 6062, 3781, 7865, 28630
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OFFSET
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1,1
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COMMENTS
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Post's tag system 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 1101 to w and deleting the first three letters.
The empty word is included in the count.
The orbit of the word (100)^n for n=110 dies after 43913328040672 iterations. The longest word in the orbit is 31299218, which appeared at iteration 14392308412264. See also A291792. - Lars Blomberg, Oct 04, 2017
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LINKS
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N. J. A. Sloane, Three (No, 8) Lovely Problems from the OEIS, Experimental Mathematics Seminar, Rutgers University, Oct 05 2017, Part I, Part 2, Slides. (Mentions this sequence)
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FORMULA
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Using Excel, trendlines were created for the preperiod of the Post Tag and Watanabe Tag systems as follows:
A284119: y = 8.6528*x^2.0831, R^2 = 0.478.
A292090: y = 8.5595*x^2.1033, R^2 = 0.472.
Although the error value is rather large, the curves are quite similar. (End)
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EXAMPLE
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For n = 2 the orbit of (100)^2 = 100100 consists of a preperiod of length 15, followed by a periodic portion of length 6:
Preperiod:
100100,
1001101,
11011101,
111011101,
0111011101,
101110100,
1101001101,
10011011101,
110111011101,
1110111011101,
01110111011101,
1011101110100,
11011101001101,
111010011011101,
0100110111011101,
followed by the period:
(011011101110100,
01110111010000,
1011101000000,
11010000001101,
100000011011101,
0000110111011101)
(repeat)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Edited by N. J. A. Sloane, Jul 29 2017. Added "escape clause" to the definition, Apr 19 2018.
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STATUS
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approved
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