{"schema":"vela.problem-packet.v0.1","problem":265,"statement":"Let $1\\leq a_1<a_2<\\cdots$ be an increasing sequence of integers. How fast can $a_n\\to \\infty$ grow if\\[\\sum\\frac{1}{a_n}\\quad\\textrm{and}\\quad\\sum\\frac{1}{a_n-1}\\]are both rational?","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)"}