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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.
- Borwein, van der Poorten, Shallit, and Zudilin, "Neverending Fractions," Cambridge University Press, 2014.

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

- 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

J.P. Martin-Flatin