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

Offset

1

Links

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

Index entries for sequences that are fixed points of mappings

Formula

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

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

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

Example

0->010->010100010->

Mathematica

t = Nest[Flatten[# /. {0->{0, 1, 0}, 1->{1, 0, 0}}] &, {0}, 5] (*A189668*)
f[n_] := t[[n]]
Flatten[Position[t, 0]] (*A189669*)
Flatten[Position[t, 1]] (*A189670*)
s[n_] := Sum[f[i], {i, 1, n}]; s[0] = 0;
Table[s[n], {n, 1, 120}] (*A189671*)

Crossrefs

Cf. A189628, A189669, A189670, A189671, A285347.

Sequence in context: A353674 A288512 A157687 * A353525 A353529 A286907

Adjacent sequences: A189665 A189666 A189667 * A189669 A189670 A189671

Keyword

nonn

Author

Clark Kimberling, Apr 25 2011

Status

approved