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).


function hiter()
  hammings = {1}
  prev, vals = {1, 1, 1}
  index = 1
  local function nextv()
    local n, v = 1, hammings[prev[1]]*2
	if hammings[prev[2]]*3 < v then n, v = 2, hammings[prev[2]]*3 end
	if hammings[prev[3]]*5 < v then n, v = 3, hammings[prev[3]]*5 end
	prev[n] = prev[n] + 1
	if hammings[index] == v then return nextv() end
	index = index + 1
	hammings[index] = v
	return v
  end
  return nextv
end
 
j = hiter()
for i = 1, 20 do
  print(j())
end
n, l = 0, 0
while n < 2^31 do n, l = j(), n end
print(l)