{"schema":"vela.problem-packet.v0.1","problem":346,"statement":"Let $A=\\{1\\leq a_1< a_2<\\cdots\\}$ be a set of integers such that $A\\backslash B$ is complete for any finite subset $B$ and $A\\backslash B$ is not complete for any infinite subset $B$. (Here 'complete' means all sufficiently large integers can be written as a sum of distinct members of the sequence.)Is it true that if $a_{n+1}/a_n \\geq 1+\\epsilon$ for some $\\epsilon>0$ and all $n$ then\\[\\lim_n \\frac{a_{n+1}}{a_n}=\\frac{1+\\sqrt{5}}{2}?\\]","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[{"id":"att_0b0c5965a1d1f51b","kind":"dead_end","claim":"attempted via frontier 'additive-basis' (transfer_strength=none) -> no_progress","grade":"honest_null","gateStatus":"needs_verification","superseded":false}],"velaLean":[],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}