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A042942 From substitutional generation of Kolakoski sequence (A000002). 12
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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.

FORMULA

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

CROSSREFS

Cf. A000002, A001083.

Sequence in context: A260600 A119737 A038718 * A256968 A005687 A164139

Adjacent sequences:  A042939 A042940 A042941 * A042943 A042944 A042945

KEYWORD

nonn,nice,easy

AUTHOR

David W. Wilson

STATUS

approved

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Last modified May 16 03:04 EDT 2022. Contains 353687 sequences. (Running on oeis4.)