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).


hamming: function [limit][
    if limit=1 -> return 1
    h: map 0..limit-1 'z -> 1
    x2: 2, x3: 3, x5: 5
    i: 0, j: 0, k: 0
 
    loop 1..limit-1 'n [
        set h n min @[x2 x3 x5]
        if x2 = h\[n] [
            i: i + 1
            x2: 2 * h\[i]
        ]
        if x3 = h\[n] [
            j: j + 1
            x3: 3 * h\[j]
        ]
        if x5 = h\[n] [
            k: k + 1
            x5: 5 * h\[k]
        ]
    ]
    last h
]
print map 1..20 => hamming
print hamming 1691
print hamming 1000000