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Search: id:A022003
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| A022003 |
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Decimal expansion of 1/999. |
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+0
11
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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; cons; graph; listen)
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OFFSET
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0,1
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COMMENT
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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 (FrankTAW(AT)Netscape.net), Nov 07 2006
a(n) = A130196(n) - A131534(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 12 2009]
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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 (ppl(AT)spl.at), 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 (Hieronymus.Fischer(AT)gmx.de), May 29 2007
a(n)=(1+(-1)^Fib(n+1))/2, where Fib(n)=A000045(n). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 14 2007
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PROGRAM
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(PARI) a(n)=n%3==2 [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), 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: A030315 A080887 A099395 this_sequence A131531 A144604 A022926
Adjacent sequences: A022000 A022001 A022002 this_sequence A022004 A022005 A022006
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KEYWORD
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nonn,cons,new
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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