A111090 Successive generations of an alternating Kolakoski rule.

1, 2, 11, 21, 112, 2122, 1121122, 2122121122, 1121122122121122, 212212112212211211212211, 112112212212112212211212212112112212

Offset

1,2

Comments

Strings are obtained using the Kolakoski substitution and the additional rule: start with 1 if previous string begins with 2, start with 2 if previous string begins with 1.

a(n+1) > a(n), and a(n) is always composed of 1s and 2s, hence a subsequence of A007931. - Charles R Greathouse IV, Nov 20 2024

Links

Table of n, a(n) for n=1..11.

Formula

As n grows a(2n-1) converges toward A025142 (red as a word) and a(2n) converges toward A025143. Conjecture : a(n) is asymptotic to c*(3/2)^n for some c.

Example

1-->2-->11-->21-->112-->2122

Crossrefs

Subsequence of A007931.

Cf. A111081, A000002.

Sequence in context: A113721 A127199 A085652 * A111081 A218340 A018491

Adjacent sequences: A111087 A111088 A111089 * A111091 A111092 A111093

Keyword

nonn,easy

Author

Benoit Cloitre, Oct 12 2005

Status

approved