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%I #19 Nov 01 2016 02:38:10
%S 2,1,2,1,5,3,12,9,19,16,38,20,59,42,104,65,213,111,400,245,765,439,
%T 1563,820,3046,1731,5955,3292,12078,6343,23841,13090,47204,25534,
%U 95140,50154
%N Number of strings of length n in {2,3}* for which at least one of tail(2 S) > tail(S) and tail(3 S) > tail(S) holds.
%C 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 The "tail length" tail(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; tail(S) is the number of terms that are appended to S before a 1 is reached.
%C No example is known where both tail(2 S) > tail(S) and tail(3 S) > tail(S) hold.
%H 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 [math.CO], Dec 25 2012.
%H 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.
%e Tail(22322)=2, tail(222322)=8, tail(322322)=2, so 22322 is counted in a(5).
%K nonn,more
%O 1,1
%A _Benjamin Chaffin_, Oct 02 2012
%E a(31)-a(36) from _Lars Blomberg_, Nov 01 2016
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