11 problems

Golden-ratio formulas. For every $n\geq 1$,

Kimberling's conjecture. The set $S$ consists precisely of those natural numbers $n$ for which this new expression is an integer.

Discrepancy-order conjecture. For $m e 0$,

Complete quasi-equidistribution claim. The Hammersley point set in base $$ is completely quasi-equidistributed in base $2$.

Let $\operatorname{Li}_n(z)$ denote the polylogarithm of positive integer order $n$, let … and let $\textsf{CMZV}^{5}_{n}$ denote the space of cyclotomic multiple zeta values of we…

Generalized Beatty conjecture. The positions at which the $1$'s occur in the column of digit $i$ are given by unions of generalized Beatty sequences.

Let $A_{n+1}$ be the matrix whose characteristic equation is denoted by $Q_{n+1}(x)$, and let $(x-1)^{n+1}_{F}$ denote the Golden Binomial. Characteristic-polynomial conjecture. Th…

Let $S_c$ be the row containing the exiled queen in column $c$, and let $\phi=(1+\sqrt{5})/2$ be the golden ratio. Two-line approximation conjecture. There are constants…

Baruchel's conjecture. The digit $d_0(N)=1$ if and only if

Enumeration conjecture. The sequence $(u_n)$ is an enumeration of $\mathbb{Q}(\phi)^+$.

Generalized Fibonacci-ratio convergence conjecture. There is a converging sequence of some generalized Fibonacci ratios, given the difference between consecutive ratios, including…