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On the increases of the sequence \(\lfloor k\sqrt n \rfloor\). (English) Zbl 1335.11017

In the paper an explicit formula for all increases of the sequence \(\lfloor k\sqrt n \rfloor\) for any fixed positive integer \(k\) is given. For certain values of \(k\) simplified expressions for the increases are specified. For instance, for \(k=2\) the jumps are for \(n\)’s of the form \(i^2\pm1\) for some \(i\). Upper and lower bounds for the distance between increases are also provided.

MSC:

11B83 Special sequences and polynomials
11A25 Arithmetic functions; related numbers; inversion formulas

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