A284121 Period of orbit of Post's tag system applied to the word (100)^n (version 1), or -1 if the orbit increases without limit.

2, 6, 6, 6, 1, 10, 28, 6, 10, 6, 6, 6, 1, 1, 6, 28, 10, 6, 10, 6, 6, 1, 6, 6, 1, 6, 6, 6, 6, 6, 6, 52, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 28, 6, 1, 1, 28, 6, 6, 6, 6, 6, 1, 6, 6, 6, 10, 6, 6, 6, 6, 1, 6, 1, 6, 6, 6, 6, 1, 6, 6, 6, 1, 6, 6, 6, 1, 10, 1, 10, 6, 6

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 a(n)=1 if the orbit ends at the empty word. On the other hand, Asveld defines a(n) to be zero if that happens, which gives a different sequence, A291793. - N. J. A. Sloane, Sep 04 2017

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.

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. So a(2) = 6.

Crossrefs

Cf. A284116, A284119, A291792, A291793.

Sequence in context: A069806 A123945 A291793 * A198102 A097466 A259311

Adjacent sequences: A284118 A284119 A284120 * A284122 A284123 A284124

Keyword

nonn

Author

Jeffrey Shallit, Mar 20 2017

Extensions

Edited by N. J. A. Sloane, Jul 29 2017

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

Status

approved