

A287106


Positions of 1 in A287104.


5



1, 4, 6, 8, 10, 13, 15, 17, 20, 22, 25, 27, 29, 32, 34, 36, 38, 41, 43, 46, 48, 50, 53, 55, 57, 59, 62, 64, 66, 69, 71, 73, 75, 78, 80, 83, 85, 87, 90, 92, 94, 96, 99, 101, 103, 106, 108, 111, 113, 115, 118, 120, 122, 124, 127, 129, 131, 134, 136, 138, 140
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OFFSET

1,2


COMMENTS

Let sigma be the defining morphism in A287104: 0>10, 1>12, 2>0.
Let u := 10, v := 12, w: = 120 be the return words of the word 1. [See Justin & Vuillon (2000) for definition of return word.  N. J. A. Sloane, Sep 23 2019]
Then
sigma(u) = vu, sigma(v) = w, sigma(w) = wu.
If we code w<>0, u<>1, v<>2, then this morphism turns into the morphism
0 > 01, 1 > 21, 2 > 0.
This is exactly the morphism which has A287072 as unique fixed point.
Since u and v have length 2 and w has length 3, this implies that the sequence d of first differences of (a(n)) equals A287072 with the projection 0 > 3, 1 > 2, 2 > 2. This gives the formula below.
(End)


LINKS



FORMULA

a(n) = 1 + Sum_{k=1..n1} d(k), where d(k) = 3 if A287072(k)=0, and d(k) = 2 otherwise, for k = 1,...,n.  Michel Dekking, Sep 16 2019


MATHEMATICA

s = Nest[Flatten[# /. {0 > {1, 0}, 1 > {1, 2}, 2 > 0}] &, {0}, 10] (* A287104 *)
Flatten[Position[s, 0]] (* A287105 *)
Flatten[Position[s, 1]] (* A287106 *)
Flatten[Position[s, 2]] (* A287107 *)


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



