My attempt at figuring out what's special about 277777788888899?

I ran across an interesting video by Numberphile about the number 277777788888899:

So I thought I'd "give it a go" ... in ruby:

per.rb

After running it a few times, to my surprise, I found 11 steps from 144983823277931:

$ ruby per.rb
Trying random number.
144983823277931 (digits: 15)
438939648 (digits: 9)
4478976 (digits: 7)
338688 (digits: 6)
27648 (digits: 5)
2688 (digits: 4)
768 (digits: 3)
336 (digits: 3)
54 (digits: 2)
20 (digits: 2)
0 (digits: 1)
Done.  Steps: 11

So yeah, that was fun.