9 problems

Let $d(n)$ be the Conway-type integer sequence. For $K\geq -1$, let … with initial domain $I_{-1}=\{1,2\}$. For each $n$, let $n_1$ and $n_2$ be the two parent spots occurring in t…

Let $d(n)$ be the Conway-type integer sequence, and let $I_K$ denote its generation domains, with $I_{-1}=\{1,2\}$. Power-of-two values conjecture. The sequence satisfies … and … T…

Finite-versus-infinite conjecture. The number of order $p$ $(\alpha,\beta)$-Conolly meta-Fibonacci recursions is finite if $\beta>0$ and infinite if $\beta=0$.

Classification conjecture. For $\beta>0$, the only 2-ary order $2$ $(\alpha,\beta)$-Conolly recurrences are exactly the recurrences listed in the source for $(\alpha,\beta)=(-2,3)$…

Uniqueness conjecture. The recursion $\langle 0;2:3;5\rangle[1,2,2,3,4]$ is the only other order $1$ $(0,1)$-Conolly recursion besides the original Conolly recursion.

Finiteness conjecture. For fixed $k$ and $p$, only finitely many $k$-ary order $p$ $(\alpha,\beta)$-Conolly recursions exist when $\beta>0$.

Existence conjecture. For each of the admissible $(\alpha,\beta)$ pairs considered in the paper, there are multiple 2-ary Conolly-like recursions in every order; in particular, the…

Uniqueness conjecture. The latter recursion is the only other order $1$ $(0,1)$-Conolly recursion.

Maternal-generation conjecture. The sequence $\mu(n)$ is defined for all positive integers $n$, and its maternal generation sequence is slow-growing. For each $g\geq 3$, the $g$th…