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A111081 Successive generations of an alternating Kolakoski rule. 3
1, 2, 11, 21, 221, 22112, 11221211, 21221121121, 2212211212212112, 1122122112122122112112122, 12112212211212212211211221211212212211, 211212211211221211211221221121221211221221211211221221121 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..12.

FORMULA

Conjecture : length of n-th string is asymptotic to c*(3/2)^n for some c.

EXAMPLE

1-->2-->11-->21-->221-->22112-->11221211

CROSSREFS

Cf. A000002, A054349.

Sequence in context: A127199 A085652 A111090 * A218340 A018491 A031010

Adjacent sequences:  A111078 A111079 A111080 * A111082 A111083 A111084

KEYWORD

nonn,base

AUTHOR

Benoit Cloitre, Oct 11 2005

STATUS

approved

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Last modified May 20 13:02 EDT 2022. Contains 353873 sequences. (Running on oeis4.)