Let's say we generate a sentence in a way like for example this: Fix an initial seed. Attach '1' at the end of the seed and compute sha256 of such a string. This hash is our first number. Now attach 2 at the end of the seed(instead of 1 like in the previous step) and compute sha256 to get our 2nd number. And so on.
Will this sequence behave randomly? Would it be possible to extract any information about the inital seed if enough numbers of the generated sequence are known? Does anything in this matter change if we decrease the size of the generated numbers by, for example, truncating the hash to a couple of the initial bytes or taking the hash modulo a very small number?