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).


function hamming() {
    var queues = {2: [], 3: [], 5: []};
    var base;
    var next_ham = 1;
    while (true) {
        yield next_ham;
 
        for (base in queues) {queues[base].push(next_ham * base)}
 
        next_ham = [ queue[0] for each (queue in queues) ].reduce(function(min, val) {
            return Math.min(min,val)
        });
 
        for (base in queues) {if (queues[base][0] == next_ham) queues[base].shift()}
    }
}
 
var ham = hamming();
var first20=[], i=1;
 
for (; i <= 20; i++) 
    first20.push(ham.next());
print(first20.join(', '));
print('...');
for (; i <= 1690; i++) 
    ham.next();
print(i + " => " + ham.next());