{"schema":"vela.problem-packet.v0.1","problem":357,"statement":"Let $1\\leq a_1<\\cdots <a_k\\leq n$ be integers such that all sums of the shape $\\sum_{u\\leq i\\leq v}a_i$ are distinct. Let $f(n)$ be the maximal such $k$.How does $f(n)$ grow? Is $f(n)=o(n)$?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[{"id":"att_68dcabac2b315cfd","kind":"dead_end","claim":"attempted via frontier 'sidon/B2' (transfer_strength=partial) -> no_progress","grade":"honest_null","gateStatus":"needs_verification","superseded":false}],"velaLean":[],"oeis":[{"id":"A364132","name":"a(n) is the smallest positive integer such that from the set {1, 2, ..., a(n)} one can choose an increasing sequence (s(1), s(2), ..., s(n)) in which every segment has a unique sum of elements.","terms":"1,2,4,5,7,10,12,13,15,18,21,24,25,29,30,33,36,38,41,47,50,52","url":"https://oeis.org/A364132"},{"id":"A364153","name":"a(n) is the smallest positive integer such that from the set {1, 2, ..., a(n)} one can choose a sequence (s(1), s(2), ..., s(n)) in which every segment has a unique sum.","terms":"1,2,3,5,6,7,9,10,12,13,14,17,18","url":"https://oeis.org/A364153"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}