2 problems

Let $z=1$, let $v=1/\phi=\phi-1$, and define $s_n$ by … where $s_1=1.91041843973790\mathbf{4}$ is the numerically computed value associated with the continued fraction, and let the…

Kimberling's conjecture. The sequence $(S(n))_{n\geq 1}$ consists precisely of the positive integers not belonging to the Beatty sequence