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A189668

Fixed point of the morphism 0->010, 1->100.

0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1

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OFFSET

LINKS

Table of n, a(n) for n=1..122.

Mazen Khodier, New Methods for Analyzing the Properties of Automatic Sequences, Master's Thesis, Univ. Waterloo (Canada 2026). See p. 27, Table 5.1.

Index entries for sequences that are fixed points of mappings

FORMULA

a(3*k-2) = a(k), a(3*k-1) = 1 - a(k), a(3*k) = 0 for k >= 1, a(0) = 0.

Conjecture: a(n) = 2*n - 1 - A285347(n).

This conjecture is correct, and proved in A285347. - Michel Dekking, Sep 07 2022

EXAMPLE

0->010->010100010->