

A026609


a(n) = number of 3's between nth 1 and (n+1)st 1 in A026600.


2



2, 1, 1, 1, 0, 2, 0, 2, 1, 1, 0, 2, 0, 2, 0, 2, 1, 1, 0, 2, 0, 2, 1, 1, 1, 0, 2, 1, 0, 2, 0, 2, 0, 2, 1, 1, 0, 2, 0, 2, 1, 1, 1, 0, 1, 2, 1, 1, 1, 0, 2, 0, 2, 1, 0, 2, 0, 2, 1, 1, 1, 0, 1, 2, 1, 1, 1, 0, 2, 0, 2, 1, 1, 0, 2, 0, 2, 0, 2, 1, 1, 1, 0, 2, 0, 2, 0, 2, 1, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

From Michel Dekking, Apr 15 2019: (Start)
(a(n)) is a morphic sequence, i.e., a lettertoletter projection of a fixed point of a morphism. This follows from a study of the return words of 1 in (a(n)): the word 1 in (a(n)) has 7 return words. These are A:=1, B:=123, C:=12, D:=13, E:=12323, F:=1233, G:=1223.
The sequence A026600 is fixed point of the 3symbol ThueMorse morphism mu given by mu: 1>123, 2>231, 3>312.
This induces a morphism beta on the return words given by beta: A>B, B>EDC, C>EA, D>FC, E>EDGDC, F>EDBC, G>EBDC.
Counting 3's in the return words yields the morphism gamma given by gamma: A>0, B>1, C>0, D>1, E>2, F>2, G>1.
Let y = EDGDCFCEBDCFC... be the unique fixed point of beta. Then clearly (a(n)) = gamma(y).
(End)
The frequencies of 0's, 1's and 2's in (a(n)) are 4/13, 5/13 and 4/13.  Michel Dekking, Apr 15 2019


LINKS

Table of n, a(n) for n=1..90.


EXAMPLE

beta(B) = mu(123) = 123231312 = EDC.


CROSSREFS

Sequence in context: A260516 A064744 A135997 * A286935 A090340 A287364
Adjacent sequences: A026606 A026607 A026608 * A026610 A026611 A026612


KEYWORD

nonn


AUTHOR

Clark Kimberling


STATUS

approved



