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).


print "The first 20 Hamming numbers are :"
for i = 1 to 20
    print Hamming(i);" ";
next i
 
print
print "H( 1691) = "; Hamming(1691)
end
 
function min(a, b)
    if a < b then return a else return b
end function
 
function Hamming(limit)
    dim h(1000000)
 
    h[0] = 1
    x2 = 2 : x3 = 3 : x5 = 5
    i  = 0 : j  = 0 : k  = 0
    for n = 1 to limit
        h[n]  = min(x2, min(x3, x5))
        if x2 = h[n] then i += 1: x2 = 2 *h[i]
        if x3 = h[n] then j += 1: x3 = 3 *h[j]
        if x5 = h[n] then k += 1: x5 = 5 *h[k]
    next n
    return h[limit -1]
end function