The power of nested references in Java regular expressions

One day it dawned upon me that I haven't seen any interesting uses for nested references just yet, so I decided to sit down and brew some interesting patterns; boy were there many.

Here's what I've published on stackoverflow so far:

• How does this regex find triangular numbers? (Bonus: power of twos)
  
• How can we match a^n b^n with Java regex? (Bonus: a^n b^n c^n)
  
• How does this Java regex detect palindromes?
  
• How does this regex replacement reverse a string? (I considered this the Holy Grail™ when I first decided to learn regex; I stupidly thought that it was impossible back then).
  

I still have a few more good ones to go.

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These aren't part of the series, but use nested references regardless:

• Split string of varying length using regex (an absolutely wonderful problem; I'd like to go back to this sometime in the future to apply new things I'd have learned by then, because the current solution is a bit convoluted).