Hamming numbers are numbers of the form  

    H = 2i × 3j × 5k
           where 
     i,  j,  k  ≥  0 

Hamming numbers   are also known as   ugly numbers   and also   5-smooth numbers   (numbers whose prime divisors are less or equal to 5).



Task

Generate the sequence of Hamming numbers, in increasing order.   In particular:

 Show the   first twenty   Hamming numbers.
 Show the   1691st   Hamming number (the last one below   231).
 Show the   one millionth   Hamming number (if the language – or a convenient library – supports arbitrary-precision integers).


Related tasks

 Humble numbers
 N-smooth numbers


References

 Wikipedia entry:   Hamming numbers     (this link is re-directed to   Regular number).
 Wikipedia entry:   Smooth number
 OEIS entry:   A051037   5-smooth   or   Hamming numbers
 Hamming problem from Dr. Dobb's CodeTalk (dead link as of Sep 2011; parts of the thread here and here).


native scala.collection.mutable.Queue
 
val hamming =
  q2 = Queue()
  q3 = Queue()
  q5 = Queue()
 
  def enqueue( n ) =
    q2.enqueue( n*2 )
    q3.enqueue( n*3 )
    q5.enqueue( n*5 )
 
  def stream =
    val n = min( min(q2.head(), q3.head()), q5.head() )
 
    if q2.head() == n then q2.dequeue()
    if q3.head() == n then q3.dequeue()
    if q5.head() == n then q5.dequeue()
 
    enqueue( n )
    n # stream()
 
  for q <- [q2, q3, q5] do q.enqueue( 1 )
 
  stream()