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A022003
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Decimal expansion of 1/999.
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17
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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
a(n) = A130196(n) - A131534(n). - Reinhard Zumkeller, Nov 12 2009
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LINKS
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Table of n, a(n) for n=0..98.
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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)
From Paolo P. Lava, Nov 29 2006: (Start)
a(n) = (2/3)*(cos(2*(n+1)*Pi/3) + 1/2) with n >= 0;
a(n) = 1 - ((n+1)^2 mod 3) with n >= 0;
a(n) = (1/9)*(4*(n mod 3) - 2*((n+1) mod 3) + ((n+2) mod 3) with n >= 0. (End)
From Hieronymus Fischer, May 29 2007: (Start)
a(n) = ((n+2) mod 3) mod 2.
a(n) = (1/2)*(1 - (-1)^(n + floor((n+2)/3))). (End)
a(n) = (1 + (-1)^Fibonacci(n+1))/2. - Hieronymus Fischer, Jun 14 2007
a(n) = (n^5 - n^2) mod 3. - Gary Detlefs, Mar 20 2010
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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(PARI) a(n)=n%3==2 \\ Jaume Oliver Lafont, Mar 24 2009
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CROSSREFS
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Essentially the same as A079978.
Cf. A068601.
Partial sums are given by A002264(n+1).
Sequence in context: A276397 A286747 A131531 * A353514 A144604 A022926
Adjacent sequences: A022000 A022001 A022002 * A022004 A022005 A022006
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KEYWORD
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nonn,cons
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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