Does the series of the inverse of 10 to the power of the Recaman sequence converge?

Question

I was wondering if the following series converged: $$\sum^\infty_{n=0}\frac{1}{10^{R_n}}$$ Where $R_n$ is the n-th number in the Recaman sequence. My original thoughts were that it would converge if each value of $R_n$ repeated only a finite number of times, but I realized I had no proof. All the tests I know don't apply to this series because it is not strictly increasing or decreasing, nor is it an alternating series. Can we prove that the sum converges, if yes, how so?