A286655 - OEIS

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A286655

Characteristic sequence of the Beatty sequence, A022842, of sqrt(8).

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

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OFFSET

COMMENTS

The positions of 0 are given by A286323, and of 1, by A022842.

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = 1 - floor((n+1)*(1-1/r)) + floor(n*(1-1/r)), where r = sqrt(8). [corrected by Georg Fischer, Sep 01 2022]

MATHEMATICA

r = Sqrt[8];

s = 1 - Table[Floor[(n + 1) (1 - 1/r) - Floor[n (1 - 1/r)]], {n, 1, 200}] (* A286655 *)

Flatten[Position[s, 0]] (* A286323 *)