Hacker News new | comments | ask | jobs | submit login 1/9998 = 0.0001 0002 0004 0008 0016 0032 0064 0128 0256.. (wolframalpha.com) 491 points by rsiqueira 13 hours ago | 80 comments crntaylor 13 hours ago | link 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 digits, which happens approximately when 2^k > 10^n => k > n log(10) / log(2) which comes out to 4 * log(10)/log(2) = 13.28 when n = 4. --- Another pattern can be generated from the power serie...