login
A285080
0-limiting word of the morphism 0->10, 1-> 011.
6
0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1
OFFSET
1
COMMENTS
The morphism 0->10, 1->011 has two limiting words. If the number of iterations is even, the 0-word evolves from 0 -> 10 -> 01110 -> 1001101101110 -> 0111010011011100110111001101101110; if the number of iterations is odd, the 1-word evolves from 0 -> 10 -> 01110 -> 1001101101110, as in A285083.
Let v(n) = position of n-th 1. Then v(n)/n -> (1+sqrt(5))/2, the golden ratio (A001622); see A285082.
LINKS
MATHEMATICA
s = Nest[Flatten[# /. {0 -> {1, 0}, 1 -> {0, 1, 1}}] &, {0}, 14]; (* A285080 *)
Flatten[Position[s, 0]]; (* A285081 *)
Flatten[Position[s, 1]]; (* A285082 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 19 2017
STATUS
approved