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

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

Offset

1,3

Comments

The runs of zeros in between the digit strings are given in A085296.

Links

Table of n, a(n) for n=1..105.

Formula

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.

Crossrefs

Cf. A001285 (Thue-Morse), A000108 (Catalan), A039969 (d-perfect), A085296.

Sequence in context: A027354 A192227 A102673 * A080972 A037814 A179529

Adjacent sequences: A085294 A085295 A085296 * A085298 A085299 A085300

Keyword

nonn

Author

Paul D. Hanna, Jun 24 2003

Status

approved