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s(3n)-s(3n-1), where s( ) is sequence A023633.
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%I #8 Sep 15 2022 06:28:16

%S 4,2,2,5,5,5,2,2,2,5,2,2,2,5,2,2,2,5,5,5,5,2,2,2,5,5,5,5,2,2,2,5,5,5,

%T 5,2,2,2,5,2,2,2,5,2,2,2,5,2,2,2,5,5,5,5,2,2,2,5,2,2,2,5,2,2,2,5,2,2,

%U 2,5,5,5,5,2,2,2,5,2,2,2,5,2,2,2,5,2,2,2,5,5,5,5,2,2,2,5,5,5,5

%N s(3n)-s(3n-1), where s( ) is sequence A023633.

%C From _Michel Dekking_, Sep 15 2022: (Start)

%C Let (c(n): n>=0) = 0,3,4,5,9,13,17,... be the complement of A023633, and let (b(n)) be the sequence of first differences of (c(n)). Then one sees directly from the definition of A023633 that a(n) = b(n) + 1 for all n.

%C Conjecture: (a(n)) is fixed point of the morphism

%C 2->5, 4->422, 5->5222,

%C and so (b(n)) is fixed point of the morphism 1->4, 3->311, 4->4111. (End)

%K nonn

%O 1,1

%A _Clark Kimberling_