|
| |
|
|
A287520
|
|
Start with 0 and repeatedly substitute 0->012, 1->102, 2->120.
|
|
4
|
|
|
|
0, 1, 2, 1, 0, 2, 1, 2, 0, 1, 0, 2, 0, 1, 2, 1, 2, 0, 1, 0, 2, 1, 2, 0, 0, 1, 2, 1, 0, 2, 0, 1, 2, 1, 2, 0, 0, 1, 2, 1, 0, 2, 1, 2, 0, 1, 0, 2, 1, 2, 0, 0, 1, 2, 1, 0, 2, 0, 1, 2, 1, 2, 0, 1, 0, 2, 1, 2, 0, 0, 1, 2, 0, 1, 2, 1, 0, 2, 1, 2, 0, 1, 0, 2, 0, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,3
|
|
|
COMMENTS
|
This is the fixed point of the morphism 0->012, 1->102, 2->120 starting with 0. Let u be the (nonperiodic) sequence of positions of 0, and likewise, v for 1 and w for 2; then u(n)/n -> 3, v(n)/n -> 3, w(n)/n -> 3.
It is in fact easy to see that |u(n)-3n|<3, |v(n)-3n|<3, and |w(n)-3n|<3. - Michel Dekking, Oct 02 2019
See A287385 for a guide to related sequences.
|
|
|
LINKS
|
Clark Kimberling, Table of n, a(n) for n = 1..10000
Index entries for sequences that are fixed points of mappings
|
|
|
EXAMPLE
|
First three iterations of the morphism: 012, 012102120, 012102120102012120102120012.
|
|
|
MATHEMATICA
|
s = Nest[Flatten[# /. {0->{0, 1, 2}, 1->{1, 0, 2}, 2->{1, 2, 0}}] &, {0}, 9]; (*A287520*)
Flatten[Position[s, 0]]; (* A287521 *)
Flatten[Position[s, 1]]; (* A287522 *)
Flatten[Position[s, 2]]; (* A189630, conjectured *)
|
|
|
CROSSREFS
|
Cf. A287385, A287521, A287522, A189630.
Sequence in context: A029295 A185204 A217522 * A130094 A337005 A230025
Adjacent sequences: A287517 A287518 A287519 * A287521 A287522 A287523
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
Clark Kimberling, May 30 2017
|
|
|
STATUS
|
approved
|
| |
|
|
