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%I #27 Sep 04 2019 17:23:40
%S 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,
%T 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,
%U 1,1,1,5,5,5,5,5,1,1,1,1,1,5,5,5,5,5,1
%N Kolakoski-(1,5) sequence: a(n) is length of n-th run.
%C 15555511, 155555111, 155555111115555511111 are primes.
%C 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
%H Vincenzo Librandi, <a href="/A269268/b269268.txt">Table of n, a(n) for n = 1..10000</a>
%H Michael Baake and Bernd Sing, <a href="https://arxiv.org/abs/math/0206098">Kolakoski-(3,1) is a (deformed) model set</a>, arXiv:math/0206098 [math.MG], 2002-2003.
%t 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 *)
%Y 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).
%K nonn,easy
%O 1,2
%A _Vincenzo Librandi_, Feb 25 2016
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