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).


Object subclass: Hammer [
  Hammer class >> hammingNumbers: howMany [
    |h i j k x2 x3 x5| 
      h := OrderedCollection new.
      i := 0. j := 0. k := 0.
      h add: 1.
      x2 := 2. x3 := 2. x5 := 5.
      [ ( h size) < howMany ] whileTrue: [
        |m|
        m := { x2. x3. x5 } sort first.
        (( h indexOf: m ) = 0) ifTrue: [ h add: m ].
        ( x2 = (h last) ) ifTrue: [ i := i + 1. x2 := 2 * (h at: i) ].
        ( x3 = (h last) ) ifTrue: [ j := j + 1. x3 := 3 * (h at: j) ].
        ( x5 = (h last) ) ifTrue: [ k := k + 1. x5 := 5 * (h at: k) ]. 
      ].
      ^ h sort
  ]
].
 
(Hammer hammingNumbers: 20) displayNl.
(Hammer hammingNumbers: 1690) last displayNl.