7 problems

Let $Z=(Z_t)_{t\geq 0}$ be the stable process considered in the paper, let $T$ be the associated stopping time, and let $\alpha$ be its stability index. For every $k>0$, the moment…

Let $\operatorname{sft}(n)$ denote the Syracuse falling time of an odd positive integer $n$. Large-number Syracuse falling-time conjecture. … for all odd $n\geq 2^{5000}$. This con…

Let $\operatorname{ft}(n)$ denote the falling time associated with the accelerated $3x+1$ map. Large-number falling-time conjecture. … for all $n\geq 2^{500}$. This is a strong qua…

Let $\operatorname{sft}(n)$ denote the Syracuse falling time of an odd positive integer $n$. Mersenne Syracuse falling-time conjecture. … for all $\ell\geq 4625$. The assertion agr…

Let $\operatorname{syr}$ be the Syracuse map on odd positive integers, and let $\operatorname{sft}(n)$ denote the Syracuse falling time of an odd integer $n\geq 3$, namely the leas…

Let $p_n$ denote the sequence of stopping probabilities for the random walk considered in the paper. Limit conjecture. … This is presented as the main question of the problem. The…

Let $p_n$ denote the sequence of stopping probabilities for the random walk considered in the paper. Even-index monotonicity conjecture. … The paper proves the corresponding inequa…