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).


 
For h = 1 To 20
	WScript.StdOut.Write "H(" & h & ") = " & Hamming(h)
	WScript.StdOut.WriteLine
Next
WScript.StdOut.Write "H(" & 1691 & ") = " & Hamming(1691)
WScript.StdOut.WriteLine
 
Function Hamming(l)
	Dim h() : Redim h(l) : h(0) = 1
	i = 0 : j = 0 : k = 0
	x2 = 2 : x3 = 3 : x5 = 5
	For n = 1 To l-1
		m = x2
		If m > x3 Then m = x3 End If
		If m > x5 Then m = x5 End If
		h(n) = m
		If m = x2 Then i = i + 1 : x2 = 2 * h(i) End If
		If m = x3 Then j = j + 1 : x3 = 3 * h(j) End If
		If m = x5 Then k = k + 1 : x5 = 5 * h(k) End If
	Next
	Hamming = h(l-1)
End Function
 