{"schema":"vela.problem-packet.v0.1","problem":341,"statement":"Let $A=\\{a_1<\\cdots<a_k\\}$ be a finite set of positive integers and extend it to an infinite sequence $\\overline{A}=\\{a_1<a_2<\\cdots \\}$ by defining $a_{n+1}$ for $n\\geq k$ to be the least integer exceeding $a_n$ which is not of the form $a_i+a_j$ with $i,j\\leq n$. Is it true that the sequence of differences $a_{m+1}-a_m$ is eventually periodic?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}