{"schema":"vela.problem-packet.v0.1","problem":262,"statement":"Suppose $a_1<a_2<\\cdots$ is a sequence of integers such that for all integer sequences $t_n$ with $t_n\\geq 1$ the sum\\[\\sum_{n=1}^\\infty \\frac{1}{t_na_n}\\]is irrational. How slowly can $a_n$ grow?","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)"}