{"schema":"vela.problem-packet.v0.1","problem":355,"statement":"Is there a lacunary sequence $A\\subseteq \\mathbb{N}$ (so that $A=\\{a_1<a_2<\\cdots\\}$ and there exists some $\\lambda>1$ such that $a_{n+1}/a_n\\geq \\lambda$ for all $n\\geq 1$) such that\\[\\left\\{ \\sum_{a\\in A'}\\frac{1}{a} : A'\\subseteq A\\textrm{ finite}\\right\\}\\]contains all rationals in some open interval?","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)"}