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).


10 FOR h=1 TO 20: GO SUB 1000: NEXT h
20 LET h=1691: GO SUB 1000
30 STOP 
1000 REM Hamming
1010 DIM a(h)
1030 LET a(1)=1: LET x2=2: LET x3=3: LET x5=5: LET i=1: LET j=1: LET k=1
1040 FOR n=2 TO h
1050 LET m=x2
1060 IF m>x3 THEN LET m=x3
1070 IF m>x5 THEN LET m=x5
1080 LET a(n)=m
1090 IF m=x2 THEN LET i=i+1: LET x2=2*a(i)
1100 IF m=x3 THEN LET j=j+1: LET x3=3*a(j)
1110 IF m=x5 THEN LET k=k+1: LET x5=5*a(k)
1120 NEXT n
1130 PRINT "H(";h;")= ";a(h)
1140 RETURN 