How can I generate a deterministic evenly distributed random number in a blockchain
You are looking for a Verifiable Delay Function (VDF). Roughly VDFs are functions which are hard to parallelize but easy to verify (for some sense of easy). 

One simple example is to just iterate a hash function, although this has linear verification time while more advanced functions may have sublinear verification complexity. 

Here is an overview of VDFs for deterministic unpredictable values