Sorry, but this is essentially impossible. A random sequence has no pattern to it. So beyond making a list of the elements, and then providing an "equation" that indexes into that list, you cannot do so in any intelligent way.
Yes,I am sure that someone will say why not just use a Lagrange interpolating polynomial, or some such alternative. But an interpolating polynomial of order 1e6 is useless in so many ways that I won't bother going any further down that line. Or one might think of an interpolating spline. But since an interpolant between random numbers will itself be meaningless, why bother? JUST USE AN INDEX. Anything between those elements is useless and meaningless as a prediction.