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A042942
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From substitutional generation of Kolakoski sequence (A000002).
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12
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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
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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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.
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FORMULA
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a(n) = A001083(n-2) - 1. - Andrey Zabolotskiy, Jan 10 2022
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CROSSREFS
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Cf. A000002, A001083.
Sequence in context: A260600 A119737 A038718 * A256968 A005687 A164139
Adjacent sequences: A042939 A042940 A042941 * A042943 A042944 A042945
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KEYWORD
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nonn,nice,easy
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AUTHOR
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David W. Wilson
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STATUS
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approved
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