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A292089 Numbers n such that Watanabe's 3-shift tag system {00/1011} started at the word (100)^n eventually dies (i.e., reaches the empty string). 7
5, 9, 11, 16, 20, 22, 23, 25, 37, 38, 43, 47, 61, 64, 66, 68, 71, 82, 87, 95, 100, 115, 119, 120, 123, 126, 137, 141, 142, 143, 144, 147, 149, 153, 156, 158, 164, 165, 171, 178, 179, 183, 188, 195, 196, 201, 202, 203, 205, 206, 212, 214, 216, 218, 223, 232 (list; graph; refs; listen; history; text; internal format)
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.

These are the numbers such that A292091(n)=0.

Oct 11, 2017: Lars Blomberg has found that 872 is a member of this sequence. The word (100)^872 reaches the empty string after 72392976118788 iterations. The attached graph shows the lengths of the successive words in the trajectory. - N. J. A. Sloane, Oct 13 2017

LINKS

Lars Blomberg, Table of n, a(n) for n = 1..1440

Peter R. J. Asveld, On a Post's System of Tag. Bulletin of the EATCS 36 (1988), 96-102.

Lars Blomberg, Lengths of words in the trajectory of (100)^872

N. J. A. Sloane, Maple code for A291792, A284119, A291793, A284121), A291794, A291795, A291796, A292089, A292090, A292091, A292092, A292093, A292094.

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]

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 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.

Sequence in context: A314598 A209350 A314599 * A314600 A023484 A102173

Adjacent sequences:  A292086 A292087 A292088 * A292090 A292091 A292092

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Sep 10 2017

EXTENSIONS

a(8)-(18) from Lars Blomberg, Sep 14 2017

a(19) and beyond from Lars Blomberg, Apr 20 2018

STATUS

approved

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Last modified July 2 18:27 EDT 2022. Contains 355029 sequences. (Running on oeis4.)