code: import java.math.BigInteger;
  import java.util.PriorityQueue;
  
  final class Hamming {
      private static BigInteger THREE = BigInteger.valueOf(3);
      private static BigInteger FIVE = BigInteger.valueOf(5);
  
      private static void updateFrontier(BigInteger x,
                                         PriorityQueue<BigInteger> pq) {
          pq.offer(x.shiftLeft(1));
          pq.offer(x.multiply(THREE));
          pq.offer(x.multiply(FIVE));
      }
  
      public static BigInteger hamming(int n) {
          if (n <= 0)
              throw new IllegalArgumentException("Invalid parameter");
          PriorityQueue<BigInteger> frontier = new PriorityQueue<BigInteger>();
          updateFrontier(BigInteger.ONE, frontier);
          BigInteger lowest = BigInteger.ONE;
          for (int i = 1; i < n; i++) {
              lowest = frontier.poll();
              while (frontier.peek().equals(lowest))
                  frontier.poll();
              updateFrontier(lowest, frontier);
          }
          return lowest;
      }
  
      public static void main(String[] args) {
          System.out.print("Hamming(1 .. 20) =");
          for (int i = 1; i < 21; i++)
               System.out.print(" " + hamming(i));
          System.out.println("\nHamming(1691) = " + hamming(1691));
          System.out.println("Hamming(1000000) = " + hamming(1000000));
      }
  }
  