Determination of [nθ] by its Sequence of*Differences

Abstract

AbstractFor any real numberθletwhere [x] denotes the greatest integer not exceedingx.A method is given for computingfθfrom its first few terms. A similar method is given for computing the characteristic functiongθ(n)of[nθ]. The given methods converge rapidly, and generalize previous results of Bernoulli, Markorf, and Stolarsky. Note that either of the sequencesfθand gθdetermines the sequence[nθ] (n = 1, 2,…).