10 problems

Miller et al.'s conjecture. There exists an infinite sequence of square-free integers

Let $\mathbb K=\{k_i\}_{i\in\mathbb N}$ be the set of integers produced by the paper's iterative construction, and let … be the set of square-free, or Möbius, numbers. Auil's enume…

Let $\{k_i\}_{i\in\mathbb N}$ be the sequence of integers generated by the paper's iterative construction, let $\widetilde{B}_n$ be its associated approximating functions, and let…

Fix a base $b\geq 2$ and let $\overleftarrow{n}$ denote the integer obtained by reversing the base-$b$ digits of $n$. A square-free palindrome is a positive integer that is square-…

Let $v(n)$ denote the sum of the primes and exponents appearing in the prime factorization of $n$, and let $r_{10}(n)$ be the digit reversal of $n$ in base ten. A $v$-palindrome in…

Let the sum run over all square-free positive integers $n$. Erdős's conjecture. The number … is irrational. This conjecture concerns irrationality phenomena for series whose expone…

Let a natural number be square-free if it is divisible by no prime square. The natural density of a set of natural numbers is its limiting proportion among the first $N$ natural nu…

A walk to infinity is a sequence obtained by repeatedly appending at most a fixed positive number $N$ of digits to the right, with every resulting number belonging to the sequence…

The algorithm produces iteratively a sequence of numbers $\{k_i\}_{i\in\mathbb N}$ and functions $\{b_i\}_{i\in\mathbb N}$. A number is called square-free when it is not divisible…

The algorithm produces iteratively a sequence of numbers $\{k_i\}_{i\in\mathbb N}$ and functions $\{b_i\}_{i\in\mathbb N}$. The Möbius function is denoted by $\mu$. Square-free gen…