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Search: id:A111081
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| A111081 |
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Successive generations of an alternating Kolakoski rule. |
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3
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| 1, 2, 11, 21, 221, 22112, 11221211, 21221121121, 2212211212212112, 1122122112122122112112122, 12112212211212212211211221211212212211, 211212211211221211211221221121221211221221211211221221121
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Strings are obtained using the Kolakoski substitution and the additional rule : start with 1 if previous string ends with 2, start with 2 if previous string ends with 1. The concatenation of those strings gives 1211212212211211221211...which is A006928 word. If you replace the initial 1 with 12 you get 122112122122112112212...the infinite Kolakoski word A000002.
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FORMULA
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Conjecture : length of n-th string is asymptotic to c*(3/2)^n for some c.
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EXAMPLE
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1-->2-->11-->21-->221-->22112-->11221211
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CROSSREFS
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Cf. A000002, A054349.
Sequence in context: A127199 A085652 A111090 this_sequence A018491 A031010 A161708
Adjacent sequences: A111078 A111079 A111080 this_sequence A111082 A111083 A111084
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 11 2005
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