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%I #7 Mar 30 2012 18:36:38
%S 1,1,2,2,2,2,2,2,1,1,1,2,2,2,1,1,1,1,1,1,2,2,2,2,2,2,1,1,1,1,1,1,2,2,
%T 2,1,1,1,2,2,2,2,2,2,1,1,1,2,2,2,1,1,1,1,1,1,2,2,2,1,1,1,2,2,2,2,2,2,
%U 1,1,1,1,1,1,2,2,2,2,2,2,1,1,1,2,2,2,1,1,1,1,1,1,2,2,2,2,2,2,1,1,1,1,1,1,2
%N Nonzero residues of Catalan sequence modulo 3; related to the Thue-Morse sequence (A001285).
%C The runs of zeros in between the digit strings are given in A085296.
%F If a leading '1' is added to the Catalan sequence modulo 3, the only nonzero digit strings are {1, 1, 1, 2, 2, 2} and {2, 2, 2, 1, 1, 1}. Replacing these digit strings with their first digit, {1, 1, 1, 2, 2, 2} -> '1' and {2, 2, 2, 1, 1, 1} -> '2', then omitting all zeros, results in the Thue-Morse sequence.
%Y Cf. A001285 (Thue-Morse), A000108 (Catalan), A039969 (d-perfect), A085296.
%K nonn
%O 1,3
%A _Paul D. Hanna_, Jun 24 2003