{"schema":"vela.problem-packet.v0.1","problem":145,"statement":"Let $s_1<s_2<\\cdots$ be the sequence of squarefree numbers. Is it true that, for any $\\alpha \\geq 0$,\\[\\lim_{x\\to \\infty}\\frac{1}{x}\\sum_{s_n\\leq x}(s_{n+1}-s_n)^\\alpha\\]exists?","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"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}