Interesting numbers found by making a little program meself (the iterations stop the moment a value is reached that is lower than the initial one, or higher than 1,000,000,000).

   Start  Num  Max Value   Break
--------------------------------
      27   96       9232      23
      31   91       9232      23
      47   88       9232      46
      63   88       9232      61
      71   83       9232      61
     703  132     250504     628
    1055  130     250504     628
    1407  132     250504    1256
    1583  127     250504    1256
    2111  130     250504    1256
    7279  125    1702276    3844
   10087  171    2484916    7688
   12399  122    2480056    8729
   13503  127    1052512   10696
   14695  130    2480056    8729
   15039  135    9635920   10049
   15131  127    2484916   11983
   22559  132    9635920   20098
   26623  106  106358020   26321
   31911   96  121012864   24928
   34239  150   18976192   32572
   35655  220   41163712   29405
   37503  205   35075104   21722
   41407  140    6454384   31123
   45055  181   13699096   43444
   45127  210   41163712   29405
   47867   94  121012864   24928
   50427  106  121012864   49856
   53247  106  106358020   52642
   53851   88  121012864   49856
   56095  119  106358020   52642
   56255  202   35075104   43444
   56731  101  121012864   49856
   57115  200   41163712   29405
   59903  101  106358020   52642
   60583   83  121012864   49856
   60975  207  593279152   52975
   64255  194   41163712   58810
   65307   96  521790496   51014
   67583  176   13699096   57925
   69535  171  593279152   52975
   73471   91  521790496   51014
   73755  132  139841152   65699
   75007  202   35075104   57925
   77031  145   21933016   65134
   77039  125   18976192   40667
   77671  Dno Dunno   1047216490
So 77671 hit the ceiling, as 1,047,216,490 is too high...

Even more peculiar is the number of iterations. To the left is the number of iterations it took to get below the inital value, to the right is the frequency of this happening for all initial values from 1 to 77671.
Num     Frq
------------
  1   38835
  3   19418
  6    4855
  8    4854
 11    1821
 13    2124
 16     909
 19     569
 21     803
 24     414
 26     558
 29     304
 32     226
 34     293
 37     163
 39     230
 42     121
 45     180
 47      89
 40      63
 52     103
 55      62
 57      87
 60      52
 63      35
 65      55
 68      32
 70      62
 73      31
 75      37
 78      21
 81      17
 83      22
 86      16
 88      23
 91      13
 94      15
 96      20
 99       8
101      11
104       9
106      15
109      14
112      10
114      12
117      10
119       9
122       4
125       3
127       6
130       4
132       4
135       2
140       1
143       1
145       1
150       2
163       1
171       2
176       1
181       1
194       1
200       1
202       2
205       1
207       1
210       1
220       1