

A326420


Fixed point of the morphism 1>13, 2>132, 3>1322.


2



1, 3, 1, 3, 2, 2, 1, 3, 1, 3, 2, 2, 1, 3, 2, 1, 3, 2, 1, 3, 1, 3, 2, 2, 1, 3, 1, 3, 2, 2, 1, 3, 2, 1, 3, 2, 1, 3, 1, 3, 2, 2, 1, 3, 2, 1, 3, 1, 3, 2, 2, 1, 3, 2, 1, 3, 1, 3, 2, 2, 1, 3, 1, 3, 2, 2, 1, 3, 2, 1, 3, 2, 1, 3, 1, 3, 2, 2, 1, 3, 1, 3, 2, 2, 1, 3, 2
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OFFSET

1,2


COMMENTS

The standard form of this sequence, obtained by switching 2 and 3, starts with 1, 2, 1, 2, 3, 3, 1, 2, 1, 2, 3, 3, 1, 2, 3, 1, 2, 3, 1, 2, ...
The present version has the property that
This sequence, as a word, has the remarkable property that it is also fixed point of a uniform morphism of length 3, given by 1>131, 2>132, 3>322.
For an algorithm to find this morphism, see Section V of the paper "The spectrum of dynamical systems arising from substitutions of constant length". In this particular case one can verify the truth of this property by noting that the letters 1 and 3 occur in (a(n)) exclusively in the word 13. This implies that one can move the first letter of alpha(3) to the last letter of alpha(1), where alpha is the defining morphism.


LINKS



EXAMPLE

1 > 13 > 131322 > 131322131322132132 > ....


MATHEMATICA

Nest[Flatten[ReplaceAll[#, {1>{1, 3}, 2>{1, 3, 2}, 3>{1, 3, 2, 2}}]]&, {1}, 5] (* Paolo Xausa, Nov 09 2023 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



