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A376698 a(n) is the least k >= 0 such that the k-th iterate of the run lengths transform of A376637(n) equals 1.

%I A376698 #8 Oct 03 2024 11:03:29
%S A376698 0,1,2,3,3,2,4,4,4,4,5,3,5,5,3,5,5,6,5,6,6,5,6,5,4,4,4,4,6,7,6,6,6,7,
%T A376698 7,6,6,6,7,6,7,6,6,7,7,6,6,7,5,5,5,5,5,5,5,5,7,8,7,8,7,7,7,7,8,7,8,7,
%U A376698 7,7,8,7,8,7,8,7,7,8,8,7,7,8,7,8,7,8,7
%N A376698 a(n) is the least k >= 0 such that the k-th iterate of the run lengths transform of A376637(n) equals 1.
%C A376698 For any k > 0, the value k appears 2^(k-1) times.
%H A376698 Rémy Sigrist, <a href="/A376698/b376698.txt">Table of n, a(n) for n = 1..10048</a>
%H A376698 Rémy Sigrist, <a href="/A376698/a376698.gp.txt">PARI program</a>
%F A376698 a(n) = a(A376676(n)) + 1 for any n > 1.
%e A376698 The first terms, alongside the corresponding run lengths transforms, are:
%e A376698   n   a(n)  Run lengths transforms
%e A376698   --  ----  ---------------------------------
%e A376698    1     0  1
%e A376698    2     1  2 -> 1
%e A376698    3     2  11 -> 2 -> 1
%e A376698    4     3  12 -> 11 -> 2 -> 1
%e A376698    5     3  21 -> 11 -> 2 -> 1
%e A376698    6     2  22 -> 2 -> 1
%e A376698    7     4  112 -> 21 -> 11 -> 2 -> 1
%e A376698    8     4  122 -> 12 -> 11 -> 2 -> 1
%e A376698    9     4  211 -> 12 -> 11 -> 2 -> 1
%e A376698   10     4  221 -> 21 -> 11 -> 2 -> 1
%e A376698   11     5  1121 -> 211 -> 12 -> 11 -> 2 -> 1
%e A376698   12     3  1122 -> 22 -> 2 -> 1
%e A376698   13     5  1211 -> 112 -> 21 -> 11 -> 2 -> 1
%e A376698   14     5  2122 -> 112 -> 21 -> 11 -> 2 -> 1
%e A376698   15     3  2211 -> 22 -> 2 -> 1
%e A376698   16     5  2212 -> 211 -> 12 -> 11 -> 2 -> 1
%o A376698 (PARI) \\ See Links section.
%Y A376698 Cf. A376637, A376676.
%K A376698 nonn
%O A376698 1,3
%A A376698 _Rémy Sigrist_, Oct 02 2024