Is part of Markov chain is a Markov chain?

Question

I try to solve this question:

Let X be a Markov chain and let n_r : r ≥ 0 be an unbounded increasing sequence of positive integers. Show that Y_r = X_nr constitutes a (possibly inhomogeneous) Markov chain. Find the transition matrix of Y when n_r = 2r and X is a simple random walk.

I tried to develop this equation in this way:

P(Y_r+1=i|Y₁,..,Y_r)= P(X_nr+1=i|X_n1,..,X_nr)=???= P(Y_r+1=i|Y_r)

Without success and without an idea for the rest of the question. Can someone help, please?