2 problems

Generalized 2-adic valuation conjecture. There exists a 2-adic integer $\alpha_k$ and a nonnegative integer $c_k$ such that

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