{"schema":"vela.problem-packet.v0.1","problem":489,"statement":"Let $A\\subseteq \\mathbb{N}$ be a set such that $\\lvert A\\cap [1,x]\\rvert=o(x^{1/2})$. Let\\[B=\\{ n\\geq 1 : a\\nmid n\\textrm{ for all }a\\in A\\}.\\]If $B=\\{b_1<b_2<\\cdots\\}$ then is it true that\\[\\lim \\frac{1}{x}\\sum_{b_i<x}(b_{i+1}-b_i)^2\\]exists (and is finite)?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[{"id":"att_11f8d1637a3b169d","kind":"dead_end","claim":"attempted via frontier 'sidon/B2' (transfer_strength=none) -> no_progress","grade":"honest_null","gateStatus":"needs_verification","superseded":false}],"velaLean":[],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}