Hamming numbers

Generate the sequence of hamming numbers, in increasing order.

Hamming numbers are numbers of the form:

   H = 2^i * 3^j * 5^k,

Where i,j,k >= 0; and ^ is the power operator.

Show the first twenty hamming numbers
Show the 1690'th Hamming number. (the last one under 2^31)
Show the one millionth Hamming number

Python

<lang python>from itertools import islice

def hamming2():

   \
   This version is based on a snippet from:
       http://dobbscodetalk.com/index.php?option=com_content&task=view&id=913&Itemid=85

       When expressed in some imaginary pseudo-C with automatic
       unlimited storage allocation and BIGNUM arithmetics, it can be
       expressed as:
           hamming = h where
             array h;
             n=0; h[0]=1; i=0; j=0; k=0;
             x2=2*h[ i ]; x3=3*h[j]; x5=5*h[k];
             repeat:
               h[++n] = min(x2,x3,x5);
               if (x2==h[n]) { x2=2*h[++i]; }
               if (x3==h[n]) { x3=3*h[++j]; }
               if (x5==h[n]) { x5=5*h[++k]; } 
   
   h = 1
   _h=[h]    # memoized
   multipliers  = (2, 3, 5)
   multindeces  = [0 for i in multipliers] # index into _h for multipliers
   multvalues   = [x * _h[i] for x,i in zip(multipliers, multindeces)]
   yield h
   while True:
       h = min(multvalues)
       _h.append(h)
       for (n,(v,x,i)) in enumerate(zip(multvalues, multipliers, multindeces)):
           if v == h:
               i += 1
               multindeces[n] = i
               multvalues[n]  = x * _h[i]
       # cap the memoization
       mini = min(multindeces)
       if mini >= 1000:
           del _h[:mini]
           multindeces = [i - mini for i in multindeces]
       #
       yield h</lang>

Sample output:

>>> list(islice(hamming2(), 20))
[1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 32, 36]
>>> list(islice(hamming2(), 1690, 1691))
[2125764000]
>>> list(islice(hamming2(), 1000000, 1000001))
[519381797917090766274082018159448243742493816603938969600000000000000000000000000000]
>>>