3 problems

The conjectural formulas for earliest Thue–Morse progressions.

Let $k\geq 2$ be an integer, let $a,b$ be two distinct elements of $\mathbb{F}_{2^k}^{\times}$, and let $\mathbf{u}$ be the $(a,b)$-Thue–Morse sequence. Thue–Morse Stieltjes minima…

Let $a,b$ be two distinct elements of $\mathbb{F}_2[z]\backslash\mathbb{F}_2$, and let $\mathbf{u}(z)$ be the $(a,b)$-Thue–Morse sequence. Thue–Morse continued-fraction algebraicit…