{"schema":"vela.problem-packet.v0.1","problem":962,"statement":"Let $k(n)$ be the maximal $k$ such that there exists $m\\leq n$ such that each of the integers\\[m+1,\\ldots,m+k\\]are divisible by at least one prime $>k$. Estimate $k(n)$ - in particular, is it true that\\[\\log k(n) \\leq (\\log n)^{1/2+o(1)}?\\]","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A327909","name":"a(n) is the smallest start of a run of n or more integers having a prime factor greater than n.","terms":"2,5,13,19,55,65,113,151,151,226,364,406,736,736,1057,1057,1409,1409,2059,2059,2313,2313,2313,2313,2313,2313,2313,6007,69","url":"https://oeis.org/A327909"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}