

A292094


Consider Watanabe's 3shift tag system {00/1011} applied to the word (100)^n; a(n) = position of the longest word in the orbit, or 1 if the orbit is unbounded.


7



138, 133, 10, 121, 24, 215, 36, 333, 38, 407, 4429, 343, 1338, 85, 720, 1023, 420, 105, 118, 2259, 33530, 328, 6250, 1515, 370, 9729, 2059, 825, 6282, 309, 310620, 20089, 10014, 187, 12069, 1101, 21756, 2359, 1253, 53811, 7277, 598, 103772, 1275, 5584, 269
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OFFSET

1,1


COMMENTS

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.


LINKS

Lars Blomberg, Table of n, a(n) for n = 1..6080
Peter R. J. Asveld, On a Post's System of Tag. Bulletin of the EATCS 36 (1988), 96102.
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. 8399. [Annotated scanned copy]


EXAMPLE

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]
...


CROSSREFS

Cf. A284116, A291067, A291780, A291781.
Asveld's Table 1 gives data about the behavior of Post's 3shift 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 3shift tag system {00/1011} applied to (100)^n see A292089, A292090, A292091, A292092, A292093, A292094.
Sequence in context: A300407 A122703 A200335 * A031964 A114820 A107939
Adjacent sequences: A292091 A292092 A292093 * A292095 A292096 A292097


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Sep 10 2017


EXTENSIONS

a(25)(46) from Lars Blomberg, Sep 14 2017


STATUS

approved



