RU-ALLRUSSIAN 1985 Problem 11

The sequence $\mathrm{a_1,a_2,a_3,\ldots}$ satisfies $\mathrm{a_{4n + 1} = 1}$ $\mathrm{a_{4n + 3} = 0}$ $\mathrm{a_{2n} = a_n}$ . Show that it is not periodic.