A189091 Zero-one sequence based on floor(sqrt(5)): a(A022839(k))=a(k); a(A108598(k))=1-a(k); a(1)=0.

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

Offset

1

Links

Table of n, a(n) for n=1..135.

Example

Let u=A022839=(Beatty sequence for sqrt(5)) and v=A108598=(complement of u).  Then A189091 is the sequence a given by a(1)=0 and a(u(k))=a(k); a(v(k))=1-a(k).

Mathematica

r=5^(1/2); u[n_] := Floor[n*r];  (*A022839*)
a[1] = 0; h = 128;
c = (u[#1] &) /@ Range[2h];
d = (Complement[Range[Max[#1]], #1] &)[c]; (*A108598*)
Table[a[d[[n]]] = 1 - a[n], {n, 1, h - 1}]; (*A189091*)
Table[a[c[[n]]] = a[n], {n, 1, h}]   (*A189091*)
Flatten[Position[%, 0]]  (*A189092*)
Flatten[Position[%%, 1]] (*A189093*)

Crossrefs

Cf. A188967, A189092, A189093.

Sequence in context: A298952 A123594 A286801 * A344863 A145006 A189138

Adjacent sequences: A189088 A189089 A189090 * A189092 A189093 A189094

Keyword

nonn

Author

Clark Kimberling, Apr 16 2011

Status

approved