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).


func ham_gen {
    var s = [[1], [1], [1]]
    var m = [2, 3, 5]
 
    func {
        var n = [s[0][0], s[1][0], s[2][0]].min
        { |i|
            s[i].shift if (s[i][0] == n)
            s[i].append(n * m[i])
        } << ^3
        return n
    }
}
 
var h = ham_gen()
 
var i = 20;
say i.of { h() }.join(' ')
 
{ h() } << (i+1 ..^ 1691)
say h()