3 problems

Let $(X(n))_{n\geq 0}$ and $(Y(n))_{n\geq 0}$ be the sequences defined by the recursive combinatorial-game construction in the source. Rust's conjecture. For all $n\geq 1$, … The c…

Let $(X(n))_{n\geq 0}$ and $(Y(n))_{n\geq 0}$ be the sequences defined by the recursive combinatorial-game construction in the source. Cassaigne's conjectures. For every $n\geq 1$,…

Let $T=(T(n))_{n\ge 0}$ be the Tribonacci numeration system built on the language of words over $\{0,1\}$ avoiding three consecutive ones, and let $A_T$ be the corresponding summat…