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A298231 Fixed point of the morphism 1->1221, 2->122. 1

%I #13 Jan 25 2018 03:02:34

%S 1,2,2,1,1,2,2,1,2,2,1,2,2,1,1,2,2,1,1,2,2,1,2,2,1,2,2,1,1,2,2,1,2,2,

%T 1,2,2,1,1,2,2,1,2,2,1,2,2,1,1,2,2,1,1,2,2,1,2,2,1,2,2,1,1,2,2,1,1,2,

%U 2,1,2,2,1,2,2,1,1,2,2,1,2,2,1,2,2,1,1,2,2,1,2,2,1,2,2,1,1,2,2,1,1,2,2,1,2,2,1,2,2,1,1,2,2,1,2,2,1,2,2,1,1,2,2,1,2,2,1,2,2,1,1,2,2,1,1,2,2,1,2,2,1,2,2,1,1,2,2,1,2,2,1,2,2,1,1,2,2,1,2,2,1,2,2,1,1,2,2,1,1,2,2,1,2,2,1,2,2,1,1,2,2,1,1,2,2,1,2,2,1,2,2,1,1,2,2,1,2,2,1,2,2,1,1,2,2,1,2,2,1,2,2,1,1,2,2,1,1,2,2,1,2,2,1,2,2,1,1,2,2,1,1,2,2,1,2,2,1,2,2,1,1,2,2,1,2,2,1,2,2,1

%N Fixed point of the morphism 1->1221, 2->122.

%C This is the morphism in standard form. Its mirrored version 1->211, 2->2112 has fixed point 2,1,1,2,2,1,1,2,1,1,2,1,1,2,2,1,1,2,2,1,1,2,1,1,2,... which is the sequence of first differences of A284895. This can be seen by studying A284893, the fixed point x of the morphism sigma 0->01, 1->0111. Then x is also fixed point of sigma^2: 0->010111, 1->01011101110111.

%C Note that x is a concatenation of 01 and 0111, and both words are always followed by 01, the common prefix of 01 and 0111. This implies that the two sigma^2 words induce increments in the positions of 1, which are respectively 2,1,1,2 and 2,1,1,2,1,1,2,1,1,2. This implies that 1->211, 2->2112 generates the sequence of first differences.

%t Nest[Flatten[# /. {1 -> {1, 2, 2, 1}, 2 -> {1, 2, 2}}] &, {1}, 8] (* _Michael De Vlieger_, Jan 22 2018 *)

%Y Cf. A284893, A284893, A284895.

%K nonn

%O 1,2

%A _Michel Dekking_, Jan 15 2018

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