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Search: id:A085297
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| A085297 |
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Nonzero residues of Catalan sequence modulo 3; related to the Thue-Morse sequence (A001285). |
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+0
2
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| 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, 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, 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
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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The runs of zeros in between the digit strings are given in A085296.
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FORMULA
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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.
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CROSSREFS
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Cf. A001285 (Thue-Morse), A000108 (Catalan), A039969 (d-perfect), A085296.
Sequence in context: A163529 A027354 A102673 this_sequence A080972 A037814 A118668
Adjacent sequences: A085294 A085295 A085296 this_sequence A085298 A085299 A085300
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jun 24 2003
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