OFFSET
1,1
COMMENTS
Post's tag system maps a word w over {1,2} to w', where if w begins with 1, w' is obtained by appending 11 to w and deleting the first three letters, or if w begins with 2, w' is obtained by appending 2212 to w and deleting the first three letters.
Under this Post tag system, some words when iterated end at the empty word, others go into cycles, and others may have an orbit which grows without limit. See A289670 and A289671 for the counts of the first two types. This sequence gives a list of the words that belong to cycles.
It is an important open question to decide if there is any word whose orbit grows without limit.
We work over {1,2} rather than the official alphabet {0,1} because of the prohibition in the OEIS of terms (other than 0 itself) which begin with 0.
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..253 (terms < 10^49)
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 first two cycles that one encounters when applying the Post tag system to words over the alphabet {1,2} are (21211, 112212) and (2122212111111, 22121111112212, 211111122122212, 1111221222122212, 122122212221211, 12221222121111).
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jul 29 2017
EXTENSIONS
Corrected and extended by Don Reble, Jul 31 2017
Terms sorted and more terms added by Chai Wah Wu, Aug 05 2017
STATUS
approved