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 A292093 Consider Watanabe's 3-shift tag system {00/1011} applied to the word (100)^n; a(n) = length of the longest word in the orbit, or -1 if the orbit is unbounded. 7
 59, 59, 17, 59, 31, 85, 41, 85, 49, 159, 328, 93, 93, 83, 215, 193, 121, 101, 109, 357, 781, 150, 273, 261, 171, 341, 182, 229, 551, 187, 2627, 593, 503, 187, 400, 261, 1369, 371, 226, 1045, 374, 280, 849, 375, 437, 255, 667, 365, 291, 2972, 463, 905, 631, 405 (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. 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), 96-102. 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: A054379 A278372 A273183 * A104916 A172462 A042739 Adjacent sequences:  A292090 A292091 A292092 * A292094 A292095 A292096 KEYWORD nonn AUTHOR N. J. A. Sloane, Sep 10 2017 EXTENSIONS a(25)-(54) from Lars Blomberg, Sep 14 2017 STATUS approved

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Last modified August 9 12:53 EDT 2022. Contains 356026 sequences. (Running on oeis4.)