A189723 Fixed point of the morphism 0->011, 1->101.

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

Offset

1

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.

Formula

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

Example

0->011->011101101->

Mathematica

t = Nest[Flatten[# /. {0->{0, 1, 1}, 1->{1, 0, 1}}] &, {0}, 5] (*A189723*)
f[n_] := t[[n]]
Flatten[Position[t, 0]] (*A189724*)
Flatten[Position[t, 1]] (*A189725*)
s[n_] := Sum[f[i], {i, 1, n}]; s[0] = 0;
Table[s[n], {n, 1, 120}] (*A189726*)

Crossrefs

Cf. A189628, A189724, A189725, A189726.

Sequence in context: A189576 A112448 A101264 * A095770 A285972 A275510

Adjacent sequences: A189720 A189721 A189722 * A189724 A189725 A189726

Keyword

nonn

Author

Clark Kimberling, Apr 26 2011

Status

approved