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A298231 Fixed point of the morphism 1->1221, 2->122. 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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
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.
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.
LINKS
MATHEMATICA
Nest[Flatten[# /. {1 -> {1, 2, 2, 1}, 2 -> {1, 2, 2}}] &, {1}, 8] (* Michael De Vlieger, Jan 22 2018 *)
CROSSREFS
Sequence in context: A290262 A112050 A283156 * A320473 A194884 A078401
KEYWORD
nonn
AUTHOR
Michel Dekking, Jan 15 2018
STATUS
approved

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Last modified February 29 09:21 EST 2024. Contains 370418 sequences. (Running on oeis4.)