{"schema":"vela.problem-packet.v0.1","problem":876,"statement":"Let $A=\\{a_1<a_2<\\cdots\\}\\subset \\mathbb{N}$ be an infinite sum-free set - that is, there are no solutions to\\[a=b_1+\\cdots+b_r\\]with $b_1<\\cdots<b_r<a\\in A$. How small can $a_{n+1}-a_n$ be? Is it possible that $a_{n+1}-a_n<n$?","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)"}