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).


$ limit = p1
$
$ n = 0
$ h_'n = 1
$ x2 = 2
$ x3 = 3
$ x5 = 5
$ i = 0
$ j = 0
$ k = 0
$
$ n = 1
$ loop:
$  x = x2
$  if x3 .lt. x then $ x = x3
$  if x5 .lt. x then $ x = x5
$  h_'n = x
$  if x2 .eq. h_'n
$  then
$   i = i + 1
$   x2 = 2 * h_'i
$  endif
$  if x3 .eq. h_'n
$  then
$   j = j + 1
$   x3 = 3 * h_'j
$  endif
$  if x5 .eq. h_'n
$  then
$   k = k + 1
$   x5 = 5 * h_'k
$  endif
$  n = n + 1
$  if n .le. limit then $ goto loop
$
$ i = 0
$ loop2:
$  write sys$output h_'i
$  i = i + 1
$  if i .lt. 20 then $ goto loop2
$
$ n = limit - 1
$ write sys$output h_'n