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"""368. A Kempner-like series
https://projecteuler.net/problem=368

The **harmonic series** $1 + \dfrac{1}{2} + \dfrac{1}{3} + \dfrac{1}{4} + ...$
is well known to be divergent.

If we however omit from this series every term where the denominator has a 9
in it, the series remarkably enough converges to approximately 22.9206766193.  
This modified harmonic series is called the **Kempner** series.

Let us now consider another modified harmonic series by omitting from the
harmonic series every term where the denominator has 3 or more equal
consecutive digits. One can verify that out of the first 1200 terms of the
harmonic series, only 20 terms will be omitted.  
These 20 omitted terms are:

$$\dfrac{1}{111}, \dfrac{1}{222}, \dfrac{1}{333}, \dfrac{1}{444},
\dfrac{1}{555}, \dfrac{1}{666}, \dfrac{1}{777}, \dfrac{1}{888},
\dfrac{1}{999}, \dfrac{1}{1000}, \dfrac{1}{1110}, \\\\\ \dfrac{1}{1111},
\dfrac{1}{1112}, \dfrac{1}{1113}, \dfrac{1}{1114}, \dfrac{1}{1115},
\dfrac{1}{1116}, \dfrac{1}{1117}, \dfrac{1}{1118}, \dfrac{1}{1119}$$

This series converges as well.

Find the value the series converges to.  
Give your answer rounded to 10 digits behind the decimal point.
"""
