... if anyone can point me in the right direction ...

As a first step I'd try to figure out if the data is
a.)"real" random, meaning the data is generated by a real world process with random outcome
b.) pseudo random, taken from a pseudo random number generator(pnrg) applying a given probability distribution.

If case a.) applies You could calculate the probabilty distribution and guess the next number based on the result. If case b.) applies, try to figure out the pnrg and the seed doing "some" correlation.