A269268 Kolakoski-(1,5) sequence: a(n) is length of n-th run.

1, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 1, 5, 1, 5, 1, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 1, 5, 1, 5, 1, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 1

Offset: 1

Author

Vincenzo Librandi, Feb 25 2016

Keywords

• nonn
• easy

Comments

15555511, 155555111, 155555111115555511111 are primes.

The fraction of 5s in this sequence approaches ((3+2*sqrt(2))^(1/3)+(3-2*sqrt(2))^(1/3))/4 ~ 0.588825 -- see the formula in A064353. - Ed Wynn, Sep 04 2019

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• Michael Baake and Bernd Sing, Kolakoski-(3,1) is a (deformed) model set, arXiv:math/0206098 [math.MG], 2002-2003.

Crossrefs

Cf. Kolakoski-(1,k) sequence: A000002 (k=2), A064353 (k=3), A071907 (k=4), this sequence (k=5), A269348 (k=6), A269349 (k=7), A269350 (k=8), A269351 (k=9), A269352 (k=10).

Programs

Mathematica

seed = {1, 5}; w = {}; i = 1; Do[w = Join[w, Array[seed[[Mod[i - 1, Length[seed]] + 1]] &, If[i > Length[w], seed, w][[i]]]]; i++, {n, 250}]; w (* from Ivan Neretin in similar sequences *)