# Nested Impossibilities

Algebra Level 4

$\Large 4+\frac{1}{2+\frac{1}{1+\frac{1}{3+\frac{1}{1+\frac{1}{2+\frac{1}{8+\frac{1}{\ddots} } } } } } } = \sqrt{ A}$

Find the positive integer $$A$$ in the equation above.


Details and Assumptions:

• The pattern repeats $$2,1,3,1,2,8$$ infinitely, but the $$4$$ comes only one time, i.e. in the beginning.
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