Discrepancy of the sequence \(\Big(\Big\{n{1+\sqrt{5}\over 2}\Big\}\Big)\) (Q1249598)

Let \(D^*(N)\) be the star-discrepancy of the sequence \(\Big(\Big\{n{1+\sqrt{5}\over 2}\Big\}\Big)\). We show that \[ \limsup {D^*(N)\over \log N} = {3\over 20} \Big(\log{1+\sqrt 5\over 2}\Big) ^{-1} = 0.31\cdots, \] which illustrates the fact that our sequence has smaller star-discrepancy than that of van der Corput's sequence. Our proofs involve continued fraction theory.