{"schema":"vela.problem-packet.v0.1","problem":1051,"statement":"Is it true that if $1\\leq a_1<a_2<\\cdots$ is a sequence of integers with\\[\\liminf a_n^{1/2^n}>1\\]then\\[\\sum_{n=1}^\\infty \\frac{1}{a_na_{n+1}}\\]is irrational?","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)"}