3 problems

Let $B_m$ denote the $m$th Bell number. Bell-number congruence conjecture. There are infinitely many positive integers $n$ such that … The paper reports computational examples of s…

For $x>0$, define … so that $B(n)=B_n$ for nonnegative integers $n$, where $B_n$ is the $n$-th Bell number. Bell-function concavity conjecture. The function $B(x)^{1/x}$ is log-con…

A modified ascent sequence is obtained from an ascent sequence by the modification process described in the source. For patterns $101$, $0101$, $1021$, $1102$, $1120$, and $1210$,…