{"schema":"vela.problem-packet.v0.1","problem":347,"statement":"Is there a sequence $A=\\{a_1\\leq a_2\\leq \\cdots\\}$ of integers with\\[\\lim \\frac{a_{n+1}}{a_n}=2\\]such that\\[P(A')= \\left\\{\\sum_{n\\in B}n : B\\subseteq A'\\textrm{ finite }\\right\\}\\]has density $1$ for every cofinite subsequence $A'$ of $A$?","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)"}