{"schema":"vela.problem-packet.v0.1","problem":970,"statement":"Let $h(k)$ be Jacobsthal's function, defined to as the minimal $m$ such that, if $n$ has at most $k$ prime factors, then in any set of $m$ consecutive integers there exists an integer coprime to $n$. Determine the order of magnitude of $h(k)$. In particular, is it true that\\[h(k) \\ll k^2?\\]","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A048669","name":"The Jacobsthal function g(n): maximal gap in a list of all the integers relatively prime to n.","terms":"1,2,2,2,2,4,2,2,2,4,2,4,2,4,3,2,2,4,2,4,3,4,2,4,2,4,2,4,2,6,2,2,3,4,3,4,2,4,3,4,2,6,2,4,3,4,2,4,2,4,3,4,2,4,3,4,3,4,2,6,","url":"https://oeis.org/A048669"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}