Irrational sums
Sufficient conditions for the irrationality of the sum of the series \(\sum_{n\geq 1} 1/H (f(n))\) are obtained. Here \(H(k)\) is a recurrent sequence and \(f\) is a strictly increasing function from the set of positive integers to the set of nonnegative integers. All the proofs are based on an elementary irrational criterion due to the reviewer [Glasg. Math. J. 29, 221-228 (1987; Zbl 0629.10027)]. Several analogous results are now known, due to the work of P.-G. Becker, P. Bundschuh, P. Hančl, P. Kiss, W. McDaniel, A. Pethö, T. Töpfer, K. Väänänen and the reviewer, among others.
scientific article; zbMATH DE number 894647