This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A289674 #41 Apr 07 2019 18:52:07
%S A289674 21211,112212,21211221211,112212112212,221222121111,1112212221211,
%T A289674 2122212111111,2221211112212,12111122122212,12221222121111,
%U A289674 22121111112212,122122212221211,211111122122212,1111221222122212,21211221211221211,21222122212111111,112212112212112212
%N A289674 Consider the Post tag system described in A284116 (but adapted to the alphabet {1,2}); sequence lists the words that belong to cycles.
%C A289674 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.
%C A289674 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.
%C A289674 It is an important open question to decide if there is any word whose orbit grows without limit.
%C A289674 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.
%H A289674 Chai Wah Wu, <a href="/A289674/b289674.txt">Table of n, a(n) for n = 1..253</a> (terms < 10^49)
%H A289674 Shigeru Watanabe, <a href="/A284116/a284116.pdf">Periodicity of Post's normal process of tag</a>, 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]
%e A289674 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).
%Y A289674 Cf. A284116, A284119, A284121, A289670-A289675.
%K A289674 nonn
%O A289674 1,1
%A A289674 _N. J. A. Sloane_, Jul 29 2017
%E A289674 Corrected and extended by _Don Reble_, Jul 31 2017
%E A289674 Terms sorted and more terms added by _Chai Wah Wu_, Aug 05 2017