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%I #16 Sep 03 2013 05:42:28
%S 3,3,0,9,0,9,0,9,0,9,0,6,2,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,
%T 0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,
%U 0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,0
%N Decimal expansion of 9099999999923/27500000000000.
%C The decimal expansion of the fraction 9099999999923 / 27500000000000 is 0.3309090909062909090... (with the "90" digit pairs infinitely repeating).
%C One way to write this fraction as a simple continued fraction with single-digit terms is
%C [ 0; 3, 3, 0, 9, 0, 9, 0, 9, 0, 9, 0, 6, 2,
%C 9, 0, 9, 0, 9, 0, ..., 9, 0, 9, 0, 9, 0,
%C 6, 1, 2, 6, 1, 1, 1, 9, 0, 9, 0, 5, 2, 1, 4 ]
%C where the second line contains the repeating term pair "9, 0," a total of 524727 times. The digits of the decimal expansion perfectly agree with the first two lines of the terms of the continued fraction. So we have 1049483 terms in the continued fraction with 1049468 digits of agreement.
%H Vincenzo Librandi, <a href="/A169670/b169670.txt">Table of n, a(n) for n = 0..1000</a>
%t (* Mma code from Michael Trott to check this: *)
%t cf = {0, 3, 3, 0, 9, 0, 9, 0, 9, 0, 9, 0, 6, 2,
%t Sequence @@ Flatten[Table[{9, 0}, {524727}]],
%t 6, 1, 2, 6, 1, 1, 1, 9, 0, 9, 0, 5, 2, 1, 4};
%t In[271]:= fcf = FromContinuedFraction[cf]
%t In[309]:= rds = RealDigits[fcf, 10, 1049468, 0][[1]];
%t In[311]:= Take[cf, 1049468] === rds
%t Out[311]= True (* end of program *)
%t RealDigits[9099999999923 / 27500000000000, 10, 110][[1]] (* _Vincenzo Librandi_, Sep 03 2013 *)
%Y Cf. A039662.
%K nonn,cons,nice
%O 0,1
%A _Jon E. Schoenfield_, Apr 09 2010
%E Edited by _Charles R Greathouse IV_, Aug 02 2010
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