?! The sum of powers of 2 up to 20 is 2^21-1, which is ~$20k; so not $100k, but definitely not 50 cents.
Yeah, I botched my mental math, but yours isn't quite right either, because the 141st character is 1 cent, which is 2^0. So the 20th power of two in this context is 2^19, and the sum of the powers of two up to the 19th is 2^20 - 1.
Damn. I had originally even typed it with 2^20-1 and $10k, but then second-guessed myself. (This process of me second guessing my math intuition and then making it worse is also why I didn't end up competing on the national level for my state in the high school math leagues ;P.)
What evanpw seems to be suggesting grows faster than you might think.