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 digit...

 Discovery of the First Pulsar

In 1967, British scientists found a much nearer intense radio source turning on and off with astonishing precision, its period constant to ten or more significant figures. What was it? Their first thought was that it was a message intended for us, or maybe an interstellar navigation and timing beacon for spacecraft that ply the space between the stars. They even gave it, among themselves at Cambridge University, the wry designation LGM-1 - LGM standing for Little Green Men. However, they wer...