5 problems

Let $a,b$ be parameters of a two-generator Ulam sequence $\mathcal{U}(a,b)$. Say that two such sequences follow the same pattern when their corresponding structural behavior agrees…

Let $a,b$ be relatively prime positive integers, with one of $a,b$ even. For an Ulam sequence $\mathcal{U}(a,b)$, Finch's even-term conjecture. If $a$ is even, then…

Let $a,b$ be relatively prime, with $a$ even and $b>2a$ odd. The modified Ulam sequence $\mathcal{V}(a,b)$ has explicitly listed even terms in the cases $a\in\{4,6,8,10,12,14,16\}$…

Let $a<b$ be relatively prime positive integers. Let $\mathcal{U}(a,b)$ denote the Ulam sequence generated by $a,b$, let $\mathcal{V}(a,b)$ denote the corresponding modified Ulam s…

Let $n\geqslant 5$ be odd, and let $\mathcal{V}(2,n)$ be the greedy sequence whose initial terms are $2,n$ and whose subsequent terms are the least larger integers having a unique…