KöMaL 2010 B4320

Write down the numbers $x_k=\big[k\sqrt2\,\big]$ ($k=1,2,\ldots$) in a row, and underneath, in a second row list the integers 0<$y_1$<$y_2$<... that do not occur among the numbers $x_k$. Express the difference $y_k$-$x_k$ as a function of $k$.