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A189081
Zero-one sequence based on the sequence floor(n*sqrt(2)): a(A001951(k))=a(k); a(A001952(k))=1-a(k); a(1)=0, a(2)=1.
5
0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0
OFFSET
1
EXAMPLE
Let u=A001951=(Beatty sequence for sqrt(2)) and v=A001952=(Beatty sequence for 2+sqrt(2)). Then A189081 is the sequence a given by a(u(k))=a(k); a(v(k))=1-a(k), where a(0)=0 and a(1)=1.
MATHEMATICA
r = 2^(1/2); u[n_] := Floor[r*n]; (*A001951*)
v[n_] := Floor[(2 + r) n]; (*A001952*)
a[1] = 0; a[2] = 1; h = 200;
c = Table[u[n], {n, 1, h}];
d = Table[v[n], {n, 1, h}];
Table[a[d[[n]]] = 1 - a[n], {n, 1, h - 1}]; (*A189081*)
Table[a[c[[n]]] = a[n], {n, 1, h}] (*A189081*)
Flatten[Position[%, 0]] (*A189082*)
Flatten[Position[%%, 1]] (*A189083*)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Apr 16 2011
STATUS
approved