Do you mean that x0 and x12 are lists? In that case the syntax for getting the k-th element of a list x is x[[k]].
x[k] would be interpreted as the value of the function x with k as parameter. You could use this to your advantage by specifying the function of how you want k to change:
x[k_]:=k+Exp[k] or whatever.
Then x would certainly be able to change with k! the _ after k specifies it as a variable, it is not used on the right hand side.