500 heads followed by 500 tails, realy could happen in truly random data. I think thats part of why testing for such is impossible. It would be far better to show what algorithm you are using, so that we could then invistigate it for obvious bias. Just my 2 cents.

Dictionary.com defines random as - Of or relating to a type of circumstance or event that is described by a probability distribution.

Given that definition you could just pick 1000 numbers and then make sure that they present a distribution that you expect. Good luck.