{"schema":"vela.problem-packet.v0.1","problem":663,"statement":"Let $k\\geq 2$ and $q(n,k)$ denote the least prime which does not divide $\\prod_{1\\leq i\\leq k}(n+i)$. Is it true that, if $k$ is fixed and $n$ is sufficiently large, we have\\[q(n,k)<(1+o(1))\\log n?\\]","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A391668","name":"Table read by antidiagonals. T(n,k) is the least number coprime to all numbers in [n+1, n+k].","terms":"3,5,2,5,5,3,7,7,3,2,7,7,7,7,5,11,11,11,11,5,2,11,11,11,11,5,3,3,11,11,11,11,5,5,5,2,11,11,11,11,11,11,7,7,3,13,13,13,13,","url":"https://oeis.org/A391668"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}