3 problems

Negative-column run-length conjecture. For $i<0$, there are either runs of $1$'s of length $L^{\text{P}}_{-i}$, or runs of $1$'s of length $L^{\text{P}}_{-i}$ directly followed by…

Pell-Lucas intervals conjecture. The $\Lambda^{\text{P}}_n$ are the intervals of constant expansion length of the standard silver-mean representation, and the $\Gamma^{\text{P}}_n$…

Pell-Lucas discrepancy conjecture. The natural numbers $6,12,20,26,34,\dots$ for which