Reciprocal of 19 from Sum of Powers of 2 Backwards

Theorem
The decimal expansion of the reciprocal of $19$ can be constructed by summing the powers of $2$, offset progressively backwards by $1$ digit:

1                       2                       4                      8                    16                   32                  64                128               256              512            1024           2048          4096         8192       16384      32768     65536   131072 + 262144 ...... -- .......1052631578947368421

while:
 * $\dfrac 1 {19} = 0 \cdotp \dot 05263 \, 15789 \, 47368 \, 42 \dot 1$