OFFSET
1,4
COMMENTS
A ternary analog of A059448.
Offset is 1 to avoid the ambiguity at n=0.
Inspired by Chapter 1 of Allouche and Shallit.
From Michel Dekking, Sep 30 2020: (Start)
Let tau be the "twisted" 3-symbol length 2 Thue-Morse morphism given by
tau(0) = 10, tau(1) = 21, tau (2) = 02.
The name of tau is in analogy with the comments from A297531. The "ordinary" 3-symbol length 2 Thue-Morse morphism is the morphism mu given by
mu(0) = 01, mu(1) = 12, mu(2) = 20.
The unique fixed point of mu is the sequence A071858 = 01121220...
We have mu^3 = tau^3.
The sequence a = (a(n)) satisfies
a = 0 tau(a).
This follows directly from the recursion formulas
a(2n) = a(n) + 1 mod 3, a(2n+1) = a(n).
(End)
REFERENCES
J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003.
FORMULA
a(2n) = a(n) + 1 mod 3, a(2n+1) = a(n). - Michel Dekking, Sep 30 2020
MAPLE
s1:=[];
for n from 0 to 200 do
t1:=convert(n, base, 2); t2:=subs(1=NULL, t1); s1:=[op(s1), nops(t2) mod 3]; od:
s1;
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jan 11 2011
STATUS
approved