A188432 Fixed point of the morphism 0->001, 1->01.

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

Offset

1

Comments

This is column 1 of the array A188294.

Is this A003849 with another 0 in front? - R. J. Mathar, Apr 01 2011

From Michel Dekking, Aug 27 2016: (Start)

Answer: yes. Since [-x] = -[x]-1 for all non-integer x, one has for n > 1:

[r] - [nr] - [(1-n)r] = 1 - [nr] + [(n-1)r] + 1 = 2 - ([nr]-[(n-1)r]) = A003849(n-2). (End)

Also, [ns] - [(n-1)s] where s = (3-sqrt(5))/2, therefore a Sturmian sequence with slope s. Also, a fixed point under the transformation (0 ->001, 1 -> 01). - Richard Blavy, Nov 18 2011; transformation corrected by Nathan Fox, May 03 2014

Links

Table of n, a(n) for n=1..141.

Formula

a(n) = [r] - [n*r] - [r-n*r], where r = (1+sqrt(5))/2.

Mathematica

r = (1 + 5^(1/2))/2 + .0000000000001;
f[n_] := Floor[r] - Floor[n*r] - Floor[r - n*r]
t = Flatten[Table[f[n], {n, 1, 200}]] (* A188432 *)
Flatten[Position[t, 0] ]  (* A026351 *)
Flatten[Position[t, 1] ]  (* A026352 *)

Crossrefs

Cf. A188294, A096270, A026351, A026352, A003849.

Sequence in context: A288216 A189628 A289239 * A282317 A212126 A144605

Adjacent sequences: A188429 A188430 A188431 * A188433 A188434 A188435

Keyword

nonn

Author

Clark Kimberling, Mar 31 2011

Extensions

Name changed by Clark Kimberling, Aug 24 2019

Status

approved