{"schema":"vela.problem-packet.v0.1","problem":875,"statement":"Let $A=\\{a_1<a_2<\\cdots\\}\\subset \\mathbb{N}$ be an infinite set such that the sets\\[S_r = \\{ a_1+\\cdots +a_r : a_1<\\cdots<a_r\\in A\\}\\]are disjoint for distinct $r\\geq 1$. How fast can such a sequence grow? How small can $a_{n+1}-a_n$ be? In particular, for which $c$ is it possible that $a_{n+1}-a_n\\leq n^{c}$?","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)"}