A042942 From substitutional generation of Kolakoski sequence (A000002).

1, 2, 4, 6, 9, 14, 22, 33, 49, 74, 112, 169, 254, 381, 573, 862, 1292, 1936, 2902, 4352, 6525, 9788, 14687, 22028, 33050, 49576, 74378, 111579, 167387, 251089, 376630, 564931, 847375, 1271058, 1906627, 2859983, 4289952, 6434942, 9652396

Offset: 1

Author

David W. Wilson

Keywords

• nonn
• nice
• easy

Comments

Generate A000002 via 2 -> 22 -> 2211 -> 221121 -> 221121221 -> ...; sequence gives lengths of successive strings.

a(n) appears to be asymptotic to c*(3/2)^n where c=1.3094... - Benoit Cloitre, Dec 18 2002

A more accurate estimate is c=1.309346948, probably correct to one unit in the last place. - Richard P. Brent, Dec 30 2016

Links

• Richard P. Brent and Judy-anne H. Osborn, Table of n, a(n) for n = 1..100 (first 69 terms from David Spies)
• Richard P. Brent and Judy-anne H. Osborn, A fast algorithm for the Kolakoski sequence, Dec. 2016.
• David Spies, Rust program for generating terms
• Eric Weisstein's World of Mathematics, Kolakoski sequence.

Crossrefs

Cf. A000002, A001083.

Formula

a(n) = A001083(n-2) - 1. - Andrey Zabolotskiy, Jan 10 2022