Generating Fraction for Lucas Numbers

Theorem
The fraction:
 * $\dfrac {199} {9899}$

has a decimal expansion which contains within it the start of the Lucas sequence:
 * $0 \cdotp 02010 \, 30407 \, 11 \ldots$

Proof
By long division:

0.0201030407111829    -- 9899 ) 199.0000000000000000       197 98       --- --         1 0200           9899         -             30100            29697            -              40300              39596              -                70400                69293                -                 11070                  9899                 -                  11710                   9899                  -                   18110                    9899                   -                    82110                    79192                    -                     29180                     19798                     -                      93820                      89091                      -                       4729

By Generating Function for Lucas Numbers:

The first few terms are contained in the decimal expansion, as long as $L_{k + 1} < 100$, where there is no carry.