|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|