Lengths of periods of continued fractions of square roots of integers
Empirical study of the period length \(T\) of the continued fractions of \(\sqrt{Q}\) (for growing integers \(Q\)) shows several strange asymptotic results, for instance, \(T\leq C \sqrt{Q}\ln Q\). These results show important differences between the statistics of the elements of the continued fractions of random real numbers and of square roots of random integers.
odd period lengths of continued fractions
scientific article; zbMATH DE number 5624151