The square root of any natural number $n$ can be expressed in the form of a continued fraction. When $n$ is a perfect square, its continued fraction expansion is trivial. But when it is not a perfect square, its continued fraction expansion is both infinite and periodic. We are interested in the latter here.

For more information, see:

- Continued fraction on Wikipedia.
- Jonathan Borwein, Alf van der Poorten, Jeffrey Shallit, and Wadim Zudilin, Neverending Fractions, Cambridge University Press, 2014.

The values presented below were computed using a Python program that I wrote in 2015.

- n = 2..1000
- n = 1001..2000
- n = 2001..3000
- n = 3001..4000
- n = 4001..5000
- n = 5001..6000
- n = 6001..7000
- n = 7001..8000
- n = 8001..9000
- n = 9001..10000