All Questions

If $S_k$ is the greedy sequence with no length-k arithmetic subsequence, (ie $S_3$ = A003278 , $S_4$ = A005837 , $S_5$ = A020655 ), is it guaranteed that any other sequence $a$ with no length-k ...

Let $\mathcal{A}$ be the set of all arithmetic progressions in $\mathbb{N}$ i.e \begin{align*} \mathcal{A} = \{a + b\mathbb{N} : a,b\in\mathbb{N}, b\neq 0\}. \end{align*} Does there exist a set $X \...