A169670 Decimal expansion of 9099999999923/27500000000000.

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, 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, 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

Offset

0,1

Comments

The decimal expansion of the fraction 9099999999923 / 27500000000000 is 0.3309090909062909090... (with the "90" digit pairs infinitely repeating).

One way to write this fraction as a simple continued fraction with single-digit terms is

[ 0; 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,

6, 1, 2, 6, 1, 1, 1, 9, 0, 9, 0, 5, 2, 1, 4 ]

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.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Mathematica

(* Mma code from Michael Trott to check this: *)
cf = {0, 3, 3, 0, 9, 0, 9, 0, 9, 0, 9, 0, 6, 2,
Sequence @@ Flatten[Table[{9, 0}, {524727}]],
6, 1, 2, 6, 1, 1, 1, 9, 0, 9, 0, 5, 2, 1, 4};
In[271]:= fcf = FromContinuedFraction[cf]
In[309]:= rds = RealDigits[fcf, 10, 1049468, 0][[1]];
In[311]:= Take[cf, 1049468] === rds
Out[311]= True (* end of program *)
RealDigits[9099999999923 / 27500000000000, 10, 110][[1]] (* Vincenzo Librandi, Sep 03 2013 *)

Crossrefs

Cf. A039662.

Sequence in context: A176276 A200701 A275408 * A372004 A341748 A120981

Adjacent sequences: A169667 A169668 A169669 * A169671 A169672 A169673

Keyword

nonn,cons,nice

Author

Jon E. Schoenfield, Apr 09 2010

Extensions

Edited by Charles R Greathouse IV, Aug 02 2010

Status

approved