6 problems

Smarandache cube-digital subsequence conjecture. All terms of the Smarandache cube-digital subsequence are of the form $D \times 10^{3k}$ where $D \in \left\{0,1,8\right\}$ and…

Let $a\in\mathbb{N}-\{0,1\}$ be an integer that is not a multiple of $10$. Let $\operatorname{APS}(a)$ denote the asymptotic phase shift of the tetration base $a$, represented as a…

Let a cryptarithmically unique prime be a prime that is the only prime among the numbers obtained by permuting its distinct decimal digits while preserving their multiplicities. Th…

Let $\langle a_1',\dots,a_l'\rangle$ be a solution of length $l\ge 2$, where a solution is a digit sequence satisfying the paper's square-digit condition. Prefix-closure conjecture…

Let a pattern be a finite sequence of digits satisfying the square-digit conditions defined in the paper, and let $l$ denote its length. The preceding discussion shows that such pa…

Let $n$ be an integer. Erdős's conjecture. The digit $2$ occurs in the ternary expansion of $2^n$ for all $n>8$. This is a specific conjecture about the digit structure of powers o…