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A022003
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Decimal expansion of 1/999.
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18
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0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1
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OFFSET
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0,1
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COMMENTS
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Expansion in any base b of 1/(b^3-1). E.g., 1/7 in base 2, 1/26 in base 3, 1/63 in base 4, etc. - Franklin T. Adams-Watters, Nov 07 2006
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LINKS
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FORMULA
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From Mario Catalani (mario.catalani(AT)unito.it), Jan 07 2003: (Start)
G.f.: x^2/(1-x^3).
a(n) = -(1/2)*((-1)^floor((2n-1)/3) + (-1)^floor((2n+1)/3)). (End)
a(n) = ((n+2) mod 3) mod 2.
a(n) = (1/2)*(1 - (-1)^(n + floor((n+2)/3))). (End)
a(n) = ((-1)^(a(n-1) + a(n-2)) + 1)/2 starting from n=3. - Adriano Caroli, Nov 21 2010
a(n) = 1 - Fibonacci(n+1) mod 2. - Gary Detlefs, Dec 26 2010
a(n) = floor((n+1)/3) - floor(n/3). - Tani Akinari, Oct 22 2012
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EXAMPLE
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0.001001001001001001001...
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MATHEMATICA
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Join[{0, 0}, RealDigits[1/999, 10, 120][[1]]] (* or *) PadRight[{}, 120, {0, 0, 1}] (* Harvey P. Dale, May 24 2012 *)
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PROG
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CROSSREFS
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Partial sums are given by A002264(n+1).
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KEYWORD
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AUTHOR
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STATUS
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approved
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