Hyatt, Matthew; Skyers, Marina On the increases of the sequence \(\lfloor k\sqrt n \rfloor\). (English) Zbl 1335.11017 Integers 15, Paper A17, 12 p. (2015). 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. Reviewer: Štefan Porubský (Praha) MSC: 11B83 Special sequences and polynomials 11A25 Arithmetic functions; related numbers; inversion formulas Keywords:floor function; greatest integer function; integer multiple of a square root Software:OEIS PDFBibTeX XMLCite \textit{M. Hyatt} and \textit{M. Skyers}, Integers 15, Paper A17, 12 p. (2015; Zbl 1335.11017) Full Text: EMIS Online Encyclopedia of Integer Sequences: Integer part of square root of n. Or, number of positive squares <= n. Or, n appears 2n+1 times. a(n) = floor(2*sqrt(n-2)).