Non-recursive random number generator

I have searched for pseudo-RNG algorithms but all I can find seem to generate the next number by using the previous result as seed. Is there a way to generate them non-recursively?

The scenario where I need this is during OpenCL concurrent programming, each thread/pixel needs an independent RNG. I tried to seed them using BIG_NUMBER + work_id, but the result has a strong visual pattern in it. I tried several different RNG algorithms and all have this problem. Apparently they only guarantee the numbers are independent if you generate recursively, but not when you use sequential numbers as seed.

So my question is: Can I generate an array of random numbers, from an array of sequential numbers, independently and constant time for each number? Or is it mathematically impossible?

As the solution to my openCL problem, I can just pre-generate a huge array of random numbers recursively first and store in GPU memory, then use them later using seed as index. But I'm curious about the question above, because it seems very possible just by doing bunch of overflow and cutoffs, according to my very simple understanding of chaos theory.