

A287072


Start with 0 and repeatedly substitute 0>01, 1>21, 2>0.


6



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



OFFSET

1,3


COMMENTS

A fixed point of the morphism 0>01, 1>21, 2>0. Let u be the sequence of positions of 0, and likewise, v for 1 and w for 2. Let U, V, W be the limits of u(n)/n, v(n)/n, w(n)/n, respectively. Then 1/U + 1/V + 1/W = 1, where
U = 3.079595623491438786010417...,
V = 2.324717957244746025960908...,
W = U + 1 = 4.079595623491438786010417....
Since the morphism 0>01, 1>21, 2>0 is the time reversal of the morphism 0>10, 1>12 2>0, which has fixed point A287104, in particular the incidence matrices of these two morphisms are equal. Thus the algebraic expressions found for U, V and W in A287104 do also apply to the U, V and W above.  Michel Dekking, Sep 15 2019
If n >=2, then u(n)  u(n1) is in {2,3,4}, v(n)  v(n1) is in {2,3}, and w(n)  w(n1) is in {3,4,5}.


LINKS



MATHEMATICA

s = Nest[Flatten[# /. {0 > {0, 1}, 1 > {2, 1}, 2 > 0}] &, {0}, 10] (* A287072 *)
Flatten[Position[s, 0]] (* A287073 *)
Flatten[Position[s, 1]] (* A287074 *)
Flatten[Position[s, 2]] (* A287075 *)


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



