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%I #15 Mar 14 2024 18:11:41
%S 1,1,2,1,2,2,1,1,2,2,1,2,1,1,2,1,2,2,1,2,1,1,2,2,1,1,2,1,2,2,1,1,2,2,
%T 1,2,1,1,2,2,1,1,2,1,2,2,1,2,1,1,2,1,2,2,1,1,2,2,1,2,1,1,2
%N Triangle read by rows, modified Thue-Morse sequence (A010060 with offset 1): change 0 to 2, else 1.
%C Row sums = A003945: (1, 3, 6, 12, 24,...).
%C Rows tend to A001285: (1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2,...).
%H Paolo Xausa, <a href="/A161175/b161175.txt">Table of n, a(n) for n = 1..8191</a> (rows 1..13 of the triangle, flattened).
%F Given A010060 starting with offset 1, change zeros to 2, retain 1's.
%F By rows, (n+1)-th row = n-th row with n-th row appended under morphism 1->2, 2->1.
%e First few rows of the triangle =
%e 1;
%e 1, 2;
%e 1, 2, 2, 1;
%e 1, 2, 2, 1, 2, 1, 1, 2;
%e 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1;
%e ...
%e Given A010060 starting with 1 (below, top row); 0->2, else 1:
%e A010060: (1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1,...)
%e A161175: (1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1,...)
%e Triangle read by rows, row 4 = (1, 2, 2, 1, 2, 1, 1, 2) = (2, 1, 1, 2) appended to the right of (1, 2, 2, 1).
%t ReplaceAll[ThueMorse[Range[127]],0->2] (* _Paolo Xausa_, Dec 18 2023 *)
%Y Cf. A010060, A001285, A003945
%K nonn,tabf
%O 1,3
%A _Gary W. Adamson_, Jun 05 2009
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