{"schema":"vela.problem-packet.v0.1","problem":1005,"statement":"Let $\\frac{a_1}{b_1},\\frac{a_2}{b_2},\\ldots$ be the Farey fractions of order $n\\geq 4$. Let $f(n)$ be the largest integer such that if $1\\leq k<l\\leq k+f(n)$ then $\\frac{a_k}{b_k}$ and $\\frac{a_l}{b_l}$ are similarly ordered - in other words,\\[(a_k-a_l)(b_k-b_l)\\geq 0.\\]Estimate $f(n)$ - in particular, is there a constant $c>0$ such that $f(n)=(c+o(1))n$ for all large $n$?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A386893","name":"Minimal number of Farey fractions in between two fractions that are not similarly ordered.","terms":"2,3,3,4,3,3,4,5,4,5,5,5,5,6,6,7,6,7,7,8,7,7,8,8,8,9,9,10,9,10,10,11,10,11,11,12,11,12,12,14,12,13,13,15,13,13,14,15,14,1","url":"https://oeis.org/A386893"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}