{"schema":"vela.problem-packet.v0.1","problem":264,"statement":"Let $a_n$ be a sequence of positive integers such that for every bounded sequence of integers $b_n$ (with $a_n+b_n\\neq 0$ and $b_n\\neq 0$ for all $n$) the sum\\[\\sum \\frac{1}{a_n+b_n}\\]is irrational. Are $a_n=2^n$ or $a_n=n!$ examples of such a sequence?","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)"}