I'm looking for an algorithm for computing PI that doesn't get harder the more digits computed (e.g. using factorials). Additionally, digit computation must be feasible by giving a seed of a previous computation state which essentially allows "lazy" computation of some digits with the hope of not having to store the whole number in memory. Essentially the goal is to be able to request a "number range" of digits such as provide digits 1450 through 1600 and be able to compute them at constant difficulty without having to provide all previous 1449 digits.
Computations in binary or hexadecimal are acceptable.