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A319103 a(n) is the least k > 0 such that A318928(k) = n.

%I A319103 #12 Sep 22 2018 12:14:43
%S A319103 1,3,2,4,11,18,75,621,9638,1264052,1294752365,20699153586797,
%T A319103 43409394810283725529
%N A319103 a(n) is the least k > 0 such that A318928(k) = n.
%C A319103 This sequence is well defined and infinite:
%C A319103 - for any n > 1, we can build a number m such that A318928(m) = 1 + A318928(n),
%C A319103 - let (b_1, ..., b_k) be the binary representation of n,
%C A319103 - let r_1 = 1, and for i = 1..k-1: r_{i+1} = r_i if b_{i+1} = b_i and r_{i+1} = 2 - r_i otherwise,
%C A319103 - the number m whose run lengths in binary representation are (r_1, ..., r_k) satisfies A318928(m) = 1 + A318928(n).
%C A319103 a(11) <= 42414573279593.
%C A319103 Here A318928(1) is considered to be 0, which differs from the current definition of A318928. However, I think it is quite natural to define A318928(1) to be 0. - _Hiroaki Yamanouchi_, Sep 22 2018
%H A319103 Rémy Sigrist, <a href="/A319103/a319103.gp.txt">PARI program for A319103</a>
%e A319103 The first terms of A318928, alongside the corresponding terms in this sequence, are:
%e A319103   n   A318928(n)  Corresponding terms
%e A319103   --  ----------  -------------------
%e A319103    1           0  a(0) = 1
%e A319103    2           2  a(2) = 2
%e A319103    3           1  a(1) = 3
%e A319103    4           3  a(3) = 4
%e A319103    5           2
%e A319103    6           3
%e A319103    7           1
%e A319103    8           3
%e A319103    9           3
%e A319103   10           2
%e A319103   11           4  a(4) = 11
%e A319103   12           2
%e A319103   13           4
%o A319103 (PARI) See Links section.
%Y A319103 Cf. A318928.
%Y A319103 See A319417, A319418 for record values in A318928.
%K A319103 nonn,base,more
%O A319103 0,2
%A A319103 _Rémy Sigrist_, Sep 10 2018
%E A319103 a(11)-a(12) from _Hiroaki Yamanouchi_, Sep 22 2018