Question 4
Let \(x_0=[\alpha]\), \(x_1=[2\alpha]-[\alpha]\), \(x_2=[3\alpha]-[2\alpha]\), \(x_4=[5\alpha]-[4\alpha]\), \(x_5=[6\alpha]-[5\alpha],\ldots\), where \(\alpha=\sqrt{2013}/\sqrt{2014}\). The value of \(x_9\) is: Here \([t]=\lfloor t\rfloor\). Editorial interpretation: the omitted index \(x_3\) follows the displayed pattern \(x_k=\lfloor(k+1)\alpha\rfloor-\lfloor k\alpha\rfloor\).