Continued fraction normality is not preserved along arithmetic progressions (Q267053)

Based on authors' abstract: Let \(\big<a_1,a_2,a_3,\dots\big>, \; a_i \in \mathbb{N},\) be the expansion of a number \(x \in [0,1)\) as a continued fraction and \(0{.}c_1c_2c_3\dots\) expansion of the same number in base \(b\). It is well known that if \(0{.}c_1c_2c_3\dots\) is normal expansion in base \(b\), then the numbers \(0{.}c_kc_{m+k}c_{2m+k}\dots\) for \(m\geq 2, k\geq 1\) are normal in base-\(b\) as well. In this paper, the authors prove that, in contrast, if a given continued fraction expansion \(\big<a_1,a_2,a_3,\dots\big>\) is normal, then for any integer \(m \geq 2, k\geq 1,\) the continued fraction \(\big<a_k,a_{m+k},a_{2m+k},\dots\big>,\) will never be normal. The bibliography contains 12 sources.