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 A085297 Nonzero residues of Catalan sequence modulo 3; related to the Thue-Morse sequence (A001285). 1

%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

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Last modified August 7 03:39 EDT 2024. Contains 375008 sequences. (Running on oeis4.)