A079730 Kolakoski variation using (1,2,3,4) starting with 1,2.

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

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