{"schema":"vela.problem-packet.v0.1","problem":208,"statement":"Let $s_1<s_2<\\cdots$ be the sequence of squarefree numbers. Is it true that, for any $\\epsilon>0$ and large $n$,\\[s_{n+1}-s_n \\ll_\\epsilon s_n^{\\epsilon}?\\]Is it true that\\[s_{n+1}-s_n \\leq (1+o(1))\\frac{\\pi^2}{6}\\frac{\\log s_n}{\\log\\log s_n}?\\]","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A005117","name":"Squarefree numbers: numbers that are not divisible by a square greater than 1.","terms":"1,2,3,5,6,7,10,11,13,14,15,17,19,21,22,23,26,29,30,31,33,34,35,37,38,39,41,42,43,46,47,51,53,55,57,58,59,61,62,65,66,67,","url":"https://oeis.org/A005117"},{"id":"A076259","name":"Gaps between squarefree numbers: a(n) = A005117(n+1) - A005117(n).","terms":"1,1,2,1,1,3,1,2,1,1,2,2,2,1,1,3,3,1,1,2,1,1,2,1,1,2,1,1,3,1,4,2,2,2,1,1,2,1,3,1,1,2,1,1,2,1,3,1,1,3,1,2,1,1,2,2,2,1,1,2,","url":"https://oeis.org/A076259"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}