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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1 LINKS 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 Cf. A189078, A189082, A189083, A188967. Sequence in context: A189576 A189723 A188260 * A189727 A225181 A226162 Adjacent sequences:  A189078 A189079 A189080 * A189082 A189083 A189084 KEYWORD nonn AUTHOR Clark Kimberling, Apr 16 2011 STATUS approved

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