%I A022003
%S A022003 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,
%T A022003 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,
%U A022003 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
%N A022003 Decimal expansion of 1/999.
%C A022003 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
%C A022003 a(n) = A130196(n) - A131534(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Nov 12 2009]
%F A022003 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
%F A022003 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
%F A022003 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
%F A022003 a(n)=(1+(-1)^Fib(n+1))/2, where Fib(n)=A000045(n). - Hieronymus Fischer 
               (Hieronymus.Fischer(AT)gmx.de), Jun 14 2007
%o A022003 (PARI) a(n)=n%3==2 [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), 
               Mar 24 2009]
%Y A022003 Essentially the same as A079978.
%Y A022003 Cf. A068601.
%Y A022003 Partial sums are given by A002264(n+1).
%Y A022003 Sequence in context: A030315 A080887 A099395 this_sequence A131531 A144604 
               A022926
%Y A022003 Adjacent sequences: A022000 A022001 A022002 this_sequence A022004 A022005 
               A022006
%K A022003 nonn,cons,new
%O A022003 0,1
%A A022003 N. J. A. Sloane (njas(AT)research.att.com).