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A172051 Decimal expansion of 1/999999.

%I A172051 #42 Sep 08 2022 08:45:50
%S A172051 0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,
%T A172051 0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,
%U A172051 0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0
%N A172051 Decimal expansion of 1/999999.
%C A172051 Period 6: repeat [0, 0, 0, 0, 0, 1].
%H A172051 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,1).
%F A172051 a(n) = (1-((-1)^A172050(n+4)))/2. A similar formula is given by _Hieronymus Fischer_ in A022003.
%F A172051 a(n) = 1 if (n+1) mod 6 = 0 else 0.
%F A172051 a(n) = A079979(n+1). [_R. J. Mathar_, Jan 28 2010]
%F A172051 a(n) = (n-2)*(Fibonacci(n-2)-1) mod 2. [_Gary Detlefs_, Dec 29 2010]
%F A172051 a(n) = n mod (1 + (n-1) mod 3). - _Wesley Ivan Hurt_, Aug 16 2014
%F A172051 G.f.: x^5/(1-x^6). - _Vaclav Kotesovec_, Aug 18 2014
%F A172051 a(n) = binomial((5*n+10) mod 6, 5). - _Wesley Ivan Hurt_, Aug 29 2014
%F A172051 a(n) = 1 - sign((n+1) mod 6). - _Wesley Ivan Hurt_, Aug 29 2014
%F A172051 a(n) = A245477(n) - 1. - _Wesley Ivan Hurt_, Aug 29 2014
%F A172051 From _Wesley Ivan Hurt_, Jun 23 2016: (Start)
%F A172051 a(n) = a(n-6) for n>5.
%F A172051 a(n) = (3 - 3*cos(n*Pi) + 6*cos(n*Pi/3) + 6*cos((n-4)*Pi/3) - 2*sqrt(3)*sin(2*n*Pi/3) - 2*sqrt(3)*sin((1+2*n)*Pi/3))/18. (End)
%p A172051 A172051:=n->(n mod (1+((n-1) mod 3))): seq(A172051(n), n=0..100); # _Wesley Ivan Hurt_, Aug 16 2014
%t A172051 Join[{0,0,0,0,0},RealDigits[1/999999,10,120][[1]]] (* or *) PadRight[ {},120,{0,0,0,0,0,1}] (* _Harvey P. Dale_, Oct 24 2013 *)
%o A172051 (Magma) [n mod (1 + ((n-1) mod 3)) : n in [0..100]]; // _Wesley Ivan Hurt_, Aug 29 2014
%Y A172051 Cf. A022003, A172050, A245477.
%K A172051 nonn,cons,easy
%O A172051 0,1
%A A172051 _Mats Granvik_, Jan 24 2010