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a(n) is the least d > 0 such that A010060(n) = A010060(n - i*d) for i = 0..A350226(n)-1 (A010060 corresponds to the Thue-Morse sequence).
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%I #11 Dec 30 2021 14:50:24

%S 1,1,1,3,2,2,3,3,1,3,5,3,3,6,3,3,2,7,3,6,5,5,3,3,6,3,5,9,3,6,6,3,1,3,

%T 5,7,6,6,12,3,10,10,7,7,3,9,3,3,12,7,3,6,5,10,9,17,7,6,5,9,3,12,6,9,2,

%U 7,3,15,5,5,14,14,9,12,12,12,3,19,6,3,17,20

%N a(n) is the least d > 0 such that A010060(n) = A010060(n - i*d) for i = 0..A350226(n)-1 (A010060 corresponds to the Thue-Morse sequence).

%H Rémy Sigrist, <a href="/A350285/b350285.txt">Table of n, a(n) for n = 0..8191</a>

%H Rémy Sigrist, <a href="/A350285/a350285.txt">C program for A350285</a>

%F a(n) * (A350226(n) - 1) <= n.

%e For n = 21:

%e - A350226(21) = 3,

%e - the first 22 terms of A010060 are:

%e 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1

%e * * *

%e * * *

%e * * *

%e - A010060(11) = A010060(16) = A010060(21),

%e - A010060(7) = A010060(14) = A010060(21),

%e - A010060(1) = A010060(11) = A010060(21),

%e - the first differences are 5, 7 and 10,

%e - the least first difference is 5,

%e - so a(21) = 5.

%o (C) See Links section.

%Y Cf. A010060, A350226.

%K nonn

%O 0,4

%A _Rémy Sigrist_, Dec 23 2021