but ANNs are universal approximators, they dont care if a function is recursive or anything as long as it's deterministic
Here's a simple random number generator. You start with a 16 bit number x, (your internal state). At each step you update your internal state to 75x + 74 (mod 65537), and output the first digit of your internal state (your random number)
Here's a sequence of outputs: 6,5,3,3,3,5. Does this information allow you to predict the next output? No.
For example, if the generator's starting state is x=60160, then the generator's internal state evolves as follows: [60160,55558,38093,38958,38296,54183,505]. So the seventh output will be 5. However, if your generator's starting state was instead x=6, then the generator's state evolved as follows: [6,524,39374,3959,34851,57956,21332]. So the seventh output will be 2. The releationship between the first six outputs and the seventh output is not deterministic.
Your prng looks like a truncated LCG, it could be broken if enough outputs are known. For example, 16 bits could be bruteforced in this case. If the internal state have more bits, depends on how much bits do the outputs provide, you could probably break it by Lattice (https://crypto.stackexchange.com/questions/37836/problem-wit...).
For this specific generator, knowing 6 outputs is not enough to pin down the seventh output. Not by using a NN, not by brute-forcing the possible starting seeds, not by lattice methods, not by solving a linear system over a finite field. Unless you know the internal state of the generator, you won't be able to predict the seventh output. And the first 6 outputs simply don't reveal enough information to recover the internal state.