No. We can't conclude anything. Note that for each m,n>1, mn is always a composite number. So we can define a sequence which takes a constant value c1 on each composite number and another constant value c2 on prime numbers. Then we can see that each of its subsequence of the form (xmn) will converge to c1 whereas the subsequence (xp) where p runs over the prime number sets then (xp) will converge to c2. This conclude that our sequence is not convergent.