I'm on my phone at the moment, but I did something similar except avoided the counting. I have a shell function called `ct` for "climb tree" where you specify the name of the directory you want to climb to; calling it will place you in the first directory above cwd whose name matches the argument and in addition I wrote a bash completion module for it so I only have to type minimal characters. I'll post the source for both shortly.
Looks like I wrote the tab-completion script on my work machine. I don't have access to it right now, but if I remember when I do have access I'll pastebin that as well.
