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 A079730 Kolakoski variation using (1,2,3,4) starting with 1,2. 2
 1, 2, 2, 3, 3, 4, 4, 4, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 1, 2, 3, 4, 4, 1, 1, 2, 2, 3, 3, 4, 4, 4, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 1, 2, 3, 3, 4, 4, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 1, 1, 1, 1, 2, 3, 4, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(1)=1 then a(n) is the length of n-th run. This kind of Kolakoski variation using(1,2,3,4,...,m) as m grows reaches the Golomb's sequence A001462. LINKS Ivan Neretin, Table of n, a(n) for n = 1..10000 Ulrich Reitebuch, Henriette-Sophie Lipschütz, and Konrad Polthier, Visualizing the Kolakoski Sequence, Bridges Conf. Proc.; Math., Art, Music, Architecture, Culture (2023) 481-484. FORMULA Partial sum sequence is expected to be asymptotic to 5/2*n. EXAMPLE Sequence begins: 1,2,2,3,3,4,4,4,1,1,1,2,2,2,2,3,3,3,3, read it as: (1),(2,2),(3,3),(4,4,4),(1,1,1),(2,2,2,2),(3,3,3,3),... then count the terms in parentheses to get: 1,2,2,3,3,4,4,.. which is the same sequence. MATHEMATICA seed = {1, 2, 3, 4}; w = {}; i = 1; Do[ w = Join[w, Array[seed[[Mod[i - 1, Length[seed]] + 1]] &, If[i > Length[w], seed, w][[i]]]]; i++ , {n, 41}]; w CROSSREFS Cf. A000002. Sequence in context: A252759 A085654 A074719 * A035486 A282347 A172397 Adjacent sequences: A079727 A079728 A079729 * A079731 A079732 A079733 KEYWORD nonn AUTHOR Benoit Cloitre, Feb 17 2003 EXTENSIONS Corrected by Ivan Neretin, Apr 01 2015 STATUS approved

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Last modified May 25 07:15 EDT 2024. Contains 372782 sequences. (Running on oeis4.)