Curse of the Gifted: Personal Account

I am miles away from Eric or Linus, but the "curse of the gifted" is very real. Thankfully I wasn't smart or gifted enough that I could ride it for long, but when it comes to math and problem-solving I rode it well into my high school years. I never learned to do algebra "by the book," because I didn't need to. Or maybe because I wasn't smart enough to. The math teacher would teach "3x 6 = 9." Basic algebraic problem-solving says you subtract the 6 from both sides, then divide by 3. So "3...

 1/9998 Produces Binary Output

The pattern will break down once you get past 8192, which is 2^13. That means that the pattern continues for an impressive 52 significant figures (well, it actually breaks down on the 52nd digit, which will be a 3 instead of a 2). The reason it works is that 9998 = 10^4 - 2. You can expand as   1 / (10^n - 2) = 1/10^n * 1/(1 - 2/10^n) = 1/10^n * (1 2/10^n 2^2 /10^2n 2^3 /10^3n ...) which gives the observed pattern. It breaks down when 2^k has more than n digi...