Pseudo-random generator of same "family" numbers

Question

I wonder if that is possible to create a number generator that will satisfy following requirements:

1. If seed S is provided, then generator will return a number Nx that belongs to a "family" N.
2. If number produced by the generator (Nx) is provided as a seed, then generator will return a number Ny that belongs to N as well.
3. "Belongs to 'N'" means that there is a function F(x,y) that returns 'true' if numbers belong to same family N and 'false' otherwise.

Is it possible to create such a generator with the function F?

Update 1: Amount of 'families' is not known. As well as amount of values that belong to each family (generator can use numbers from whole 128 bits range for each family). Thus, numbers sets returned from different generators can have intersections (the more numbers generated the more is probability of it).

Thanks, Dmitry

Answer 1

Maybe, it's good for you

abstract class MyRandom{
   private Random rnd;
   private long startSeed;

   protected MyRandom(long seed){
       rnd = new Random(seed);
       startSeed = seed;
   }

   public long nextLong(){
      while(true){
          long nextTry = rnd.nextLong();
          if(F(startSeed, nextTry)) return nextTry;
      }

   }

   protected abstract boolean F(long n1, long n2); 
}