A189078 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)=0.

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

Offset

1

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Example

Let u=A001951=(Beatty sequence for sqrt(2)) and v=A001952=(Beatty sequence for 2+sqrt(2)).  Then A189078 is the sequence a given by a(u(k))=a(k); a(v(k))=1-a(k), where a(0)=0 and a(1)=0.

Mathematica

r = 2^(1/2); u[n_] := Floor[r*n]; (*A001951*)
v[n_] := Floor[(2 + r) n]; (*A001952*)
a[1] = 0; a[2] = 0; 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}]; (*A189078*)
Table[a[c[[n]]] = a[n], {n, 1, h}] (*A189078*)
Flatten[Position[%, 0]] (*A189079*)
Flatten[Position[%%, 1]] (*A189080*)

Crossrefs

Cf. A188967, A189079, A189080, A189081.

Sequence in context: A288226 A104121 A179770 * A257834 A173950 A157928

Adjacent sequences: A189075 A189076 A189077 * A189079 A189080 A189081

Keyword

nonn

Author

Clark Kimberling, Apr 16 2011

Status

approved