A189706 Fixed point of the morphism 0->011, 1->001.

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

Offset

1

Links

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

Index entries for 3-automatic sequences.

Index entries for sequences that are fixed points of mappings

Formula

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

Example

0->011->011001001->...

Mathematica

t = Nest[Flatten[# /. {0->{0, 1, 1}, 1->{0, 0, 1}}] &, {0}, 5] (* A189706 *)
f[n_] := t[[n]]
Flatten[Position[t, 0]] (* A189707 *)
Flatten[Position[t, 1]] (* A189708 *)
s[n_] := Sum[f[i], {i, 1, n}]; s[0] = 0;
Table[s[n], {n, 1, 120}] (* A189709 *)

Prog

(PARI) a(n) = n--; my(ret=0); while([n, r]=divrem(n, 3); r==1, ret++); (ret+r>>1)%2; \\ Kevin Ryde, Jun 02 2021

Crossrefs

Cf. A189628, A189707, A189708, A189709.

Cf. A321090, A321091, A321093, A321095, A321097.

Sequence in context: A140591 A189476 A288752 * A188321 A257628 A203568

Adjacent sequences: A189703 A189704 A189705 * A189707 A189708 A189709

Keyword

nonn

Author

Clark Kimberling, Apr 25 2011

Status

approved