login
A189091
Zero-one sequence based on floor(sqrt(5)): a(A022839(k))=a(k); a(A108598(k))=1-a(k); a(1)=0.
3
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
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
KEYWORD
nonn
AUTHOR
Clark Kimberling, Apr 16 2011
STATUS
approved