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
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Feb 17 2003
EXTENSIONS
Corrected by Ivan Neretin, Apr 01 2015
STATUS
approved