A111090 Successive generations of an alternating Kolakoski rule.

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

Offset: 1

Author

Benoit Cloitre, Oct 12 2005

Keywords

• nonn
• easy

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

Examples

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

Crossrefs

Subsequence of A007931.

Cf. A111081, A000002.

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.