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).


 
see "h(1) = 1" + nl
for nr = 1 to 19
     see "h(" + (nr+1) + ") = " + hamming(nr) + nl
next
see "h(1691) = " + hamming(1690) + nl
see nl
 
func hamming limit
     h = list(1690)
     h[1] =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]  i = i +1  x2 =2 *h[i] ok
         if x3 = h[n]  j = j +1  x3 =3 *h[j] ok
         if x5 = h[n]  k = k +1  x5 =5 *h[k] ok
     next
     hamming = h[limit]
     return hamming
 