{"schema":"vela.problem-packet.v0.1","problem":415,"statement":"For any $n$ let $F(n)$ be the largest $k$ such that any of the $k!$ possible ordering patterns appears in some sequence of $\\phi(m+1),\\ldots,\\phi(m+k)$ with $m+k\\leq n$. Is it true that\\[F(n)=(c+o(1))\\log\\log\\log n\\]for some constant $c$? Is the first pattern which fails to appear always\\[\\phi(m+1)>\\phi(m+2)>\\cdots >\\phi(m+k)?\\]Is it true that the 'natural' ordering which mimics what happens to $\\phi(1),\\ldots,\\phi(k)$ is the most likely to appear?","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)"}