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A291793 Period of orbit of Post's tag system applied to the word (100)^n (version 2), or -1 if the orbit increases without limit. 6
2, 6, 6, 6, 0, 10, 28, 6, 10, 6, 6, 6, 0, 0, 6, 28, 10, 6, 10, 6, 6, 0, 6, 6, 0, 6, 6, 6, 6, 6, 6, 52, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 28, 6, 0, 0, 28, 6, 6, 6, 6, 6, 0, 6, 6, 6, 10, 6, 6, 6, 6, 0, 6, 0, 6, 6, 6, 6, 0, 6, 6, 6, 0, 6, 6, 6, 0, 10, 0, 10, 6, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

Here, following Asveld, a(n)=0 if the orbit ends at the empty word. On the other hand, Shallit defines a(n) to be 1 if that happens, which gives a different sequence, A284121.

LINKS

Lars Blomberg, Table of n, a(n) for n = 1..6075

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

Lars Blomberg, Histogram over non-zero terms

EXAMPLE

For n = 2 the orbit of (100)^2 = 100100 consists of a preperiod of length 15, followed by a periodic portion of length 6.

CROSSREFS

Cf. A284116, A284119, A291792, A284121.

Sequence in context: A065486 A069806 A123945 * A284121 A198102 A097466

Adjacent sequences:  A291790 A291791 A291792 * A291794 A291795 A291796

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Sep 04 2017, based on Jeffrey Shallit's A284121.

EXTENSIONS

a(50)-a(83) from Lars Blomberg, Sep 08 2017

STATUS

approved

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Last modified August 18 20:02 EDT 2019. Contains 326109 sequences. (Running on oeis4.)