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A216730 List of "rotten" strings in {2,3}* (in the curling number sense).

%I A216730 #33 Sep 04 2017 16:34:39
%S A216730 22,333,32323,323232,2323232,3232323,22322232,23222322,23223223,
%T A216730 33233233,223222322,223222323,232223222,332332332,2232223222,
%U A216730 2232223223,2232223232,2322232223,2322322322,2332332332,3322332233,3323323323,22322232223,22322232232,22322232322,22322322232,22322322322,22323222322,23222322232,23223223223
%N A216730 List of "rotten" strings in {2,3}* (in the curling number sense).
%C A216730 The "curling number" k = k(S) of a string of numbers S = s(1), ..., s(m) is defined as follows. Write S as XY^k for strings X and Y (where Y has positive length) and k is maximized, i.e., k = the maximal number of repeating blocks at the end of S.
%C A216730 The "tail length" t(S) of S is defined as follows: start with S and repeatedly append the curling number (recomputing it at each step) until a 1 is reached; t(S) is the number of terms that are appended to S before a 1 is reached.
%C A216730 If a 1 is never reached, set t(S)=oo (the Curling Number Conjecture says this will never happen).
%C A216730 A sequence S in {2,3}* is called "rotten" if either of t(2S) or t(3S) (or both) is strictly less than t(S).
%C A216730 Example: S = 32323 has curling number k=2, so we get 323232; now k=3, so we get 3232323; now k=3, so we get 32323233; now k=2, so we get 323232332; now k=1 so we stop. We added 4 terms before reaching 1, so t(S)=4.
%C A216730 On the other hand, 2S = 232323 only extends to 232323321..., so t(2S)=2 which means S is rotten.
%H A216730 Benjamin Chaffin, <a href="/A216730/b216730.txt">Table of n, a(n) for n = 1..2400</a>
%H A216730 B. Chaffin, J. P. Linderman, N. J. A. Sloane and Allan Wilks, <a href="http://arxiv.org/abs/1212.6102">On Curling Numbers of Integer Sequences</a>, arXiv:1212.6102, Dec 25 2012.
%H A216730 B. Chaffin, J. P. Linderman, N. J. A. Sloane and Allan Wilks, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL16/Sloane/sloane3.html">On Curling Numbers of Integer Sequences</a>, Journal of Integer Sequences, Vol. 16 (2013), Article 13.4.3.
%H A216730 <a href="/index/Cu#curling_numbers">Index entries for sequences related to curling numbers</a>
%Y A216730 Cf. A094004, A160766, A216950.
%K A216730 nonn,base
%O A216730 1,1
%A A216730 _Benjamin Chaffin_ and _N. J. A. Sloane_, Sep 16 2012