Summing the "exactly one 42" and similar subsums of the harmonic series
Summing the "exactly one 42" and similar subsums of the harmonic series
For $b>1$ and $\alpha\beta$ a string of two digits in base $b$, let $K_1$ be the subsum of the harmonic series with only those integers having exactly one occurrence of $\alpha\beta$. We obtain a theoretical representation of such $K_1$ series which, say for $b=10$, allows computing them all to thousands …