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Let $\{a_n\}_1^\infty$ and $\{\theta_n\}_0^\infty$ be the sequences ofpartial quotients and approximation coefficients for the continued fractionexpansion of an irrational number. We will provide a function $f$ such that$a_{n+1} = f(\theta_{n\pm1},\theta_n)$. In tandem with a formula due to Dajaniand Kraaikamp, we will write $\theta_{n \pm 1}$ as a function of $(\theta_{n\mp 1}, \theta_n)$, revealing an elegant symmetry in this classical sequenceand allowing for its recovery from a pair of consecutive terms.

Symmetry in the sequence of approximation coefficients