Is there a name for random generation systems which return exactly one result for a given key?

I am looking for a random number generator which always returns the same random number for a given integer key.

For example:

KeyBasedRandomGenerator r = new KeyBasedRandomGenerator(MY_SEED);
for (int i = 0; i < 10000000; ++i)
{
    assert ( r.Get(i) == r.Get(i));
}

Is there an implementation of such systems in C# or C++? What are they called?

Is it possible to find variations which always return the same result for a range:

    assert ( r.Get(0, 15, i) == r.Get(0, 15, i));