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
```