{"schema":"vela.problem-packet.v0.1","problem":464,"statement":"Let $A=\\{n_1<n_2<\\cdots\\}\\subset \\mathbb{N}$ be a lacunary sequence (so there exists some $\\epsilon>0$ with $n_{k+1}\\geq (1+\\epsilon)n_k$ for all $k$). Must there exist an irrational $\\theta$ such that\\[\\{ \\|\\theta n_k\\| : k\\geq 1\\}\\]is not dense in $[0,1]$ (where $\\| x\\|$ is the distance to the nearest integer)?","status":"solved","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)"}