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).


dim h(1000000)
for i =1 to 20
    print hamming(i)," ";
next i
 
print
print "Hamming List First(1691)   = ",hamming(1691)
end
 
sub hamming(limit)
    local x2,x3,x5,i,j,k,n
 
    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 = i +1: x2 =2 *h(i):end if
        if x3 = h(n) then j = j +1: x3 =3 *h(j):end if
        if x5 = h(n) then k = k +1: x5 =5 *h(k):end if
    next n
    return h(limit -1)
end sub