I actually find your requirements contradictory. A valid random sequence will not generate unique values otherwise it is not random. What I mean is you don't need anything random at all you just need the numbers to be unique.
To generate a unique number per network node is pretty easy combine machine ip or mac address with time. To get time simply do System.currentTimeMillis();
to get your ip address then use the example here how to get mac address in Java. Combining these two numbers will buy you uniqueness.