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G. C. Greubel, <a href="/A189078/b189078.txt">Table of n, a(n) for n = 1..10000</a>

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_Clark Kimberling (ck6(AT)evansville.edu), _, Apr 16 2011

OEIS Server: https://oeis.org/edit/global/285

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Let u=A001951=(Beatty sequence for sqrt(2)) and v=A001952=(Beatty sequence for 2+sqrt(2)). Then A189078 is the sequence pa given by pa(u(k))=pa(k); pa(v(k))=1-pa(k), where pa(0)=0 and pa(1)=10.

allocatedZero-one sequence based on forthe Clarksequence Kimberlingfloor(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

1

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

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*)

Cf. A188967, A189079, A189080, A189081.

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Clark Kimberling (ck6(AT)evansville.edu), Apr 16 2011

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allocated for Clark Kimberling

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