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%I #8 Jan 12 2023 01:42:55
%S 0,1,3,0,2,1,5,3,6,0,4,2,7,1,9,5,15,3,10,6,12,0,8,4,14,2,11,7,13,1,17,
%T 9,29,5,23,15,27,3,18,10,30,6,20,12,24,0,16,8,28,4,22,14,26,2,19,11,
%U 31,7,21,13,25,1,33,17,57,9,45,29,53,5,39,23,63,15
%N Order of shifts of Thue-Morse sequence.
%C Let t_i be the Thue-Morse (A010060) sequence shifted by i symbols. Say t_i < t_j if t_i precedes t_j in lexicographic order. Then the paper of Cheng shows t_0 < t_1, t_3 < t_0 < t_2 < t_1, t_5 < t_3 < t_6 < t_0 < t_4 < t_2 < t_7 < t_1, etc. Concatenating all these together gives the sequence in question.
%H Yin Choi Cheng, <a href="http://math.colgate.edu/~integers/x1/x1.pdf">Order types of shifts of morphic words</a>, INTEGERS 23 (2023), Paper #A1.
%Y Cf. A010060.
%K nonn
%O 1,3
%A _Jeffrey Shallit_, Jan 11 2023
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