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
  Print "H("; H; ") = "; Func (_FnHamming(H))
Next
 
End
 
_FnHamming Param (1)
  @(0) = 1
 
  X = 2 : Y = 3 : Z = 5
  I = 0 : J = 0 : K = 0
 
  For N = 1 To a@ - 1
    M = X
    If M > Y Then M = Y
    If M > Z Then M = Z
    @(N) = M
 
    If M = X Then I = I + 1 : X = 2 * @(I)
    If M = Y Then J = J + 1 : Y = 3 * @(J)
    If M = Z Then K = K + 1 : Z = 5 * @(K)
  Next
 
Return (@(a@-1))