8 problems

Guy's conjecture. Every finite octal game has an eventually periodic Grundy sequence.

Let $n$ be a positive integer, let $c\geq \left\lceil\frac{n}{2}\right\rceil$, and let $d=n-c$. Let $\mathcal{B}(n,c,d)$ denote the specified class of binary sequences, let…

Let $(A,B)$ be the $(v/2)$-decomposition of a periodic Golay pair $\operatorname{PG}(v)$ with row sums $a$ and $b$. Equivalence is taken in the sense used for these decompositions.…

Let $\mathbf{x}$ be a sequence. The reflection complexity periodicity conjecture. … if and only if $\mathbf{x}$ is eventually periodic. One direction is known: if $\mathbf{x}$ is e…

Non-eventual periodicity conjecture. The sign behaviour of this sequence is not eventually periodic. The supplied source attributes this conjecture to GU; no resolution is stated t…

Period-set containment conjecture.

Postnikov's periodicity conjecture. For $r\geq 3$, the sequence $\{L_n\pmod{3^r}\}$ is purely periodic with period $2\cdot 3^{r-3}$.

Least-period conjecture. The least periods of the family of generalized self-shrinking sequences belong to