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A022003
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Decimal expansion of 1/999.
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13
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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
(list;
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refs;
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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). [From 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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G.f.: x^2/(1-x^3). a(n) = -(1/2)((-1)^Floor[(2n-1)/3]+(-1)^Floor[(2n+1)/3]) - Mario Catalani (mario.catalani(AT)unito.it), Jan 07 2003
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 - Paolo P. Lava, Nov 29 2006
a(n) = ((n+2) mod 3) mod 2. Also: a(n) = 1/2*(1-(-1)^(n+floor((n+2)/3))). - Hieronymus Fischer, May 29 2007
a(n) = (1+(-1)^Fib(n+1))/2, where Fib(n) = A000045(n). - 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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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 [From 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: A080887 A099395 A171588 * A131531 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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