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

Author

Jeffrey Shallit, Mar 20 2017

Keywords

• nonn

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

Examples

			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.
		

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.

Crossrefs

Cf. A284116, A284119, A291792, A291793.

Extensions

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

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