{"schema":"vela.problem-packet.v0.1","problem":276,"statement":"Is there an infinite Lucas sequence $a_0,a_1,\\ldots$ where $a_{n+2}=a_{n+1}+a_n$ for $n\\geq 0$ such that all $a_k$ are composite, and yet no integer has a common factor with every term of the sequence?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}