{"schema":"vela.problem-packet.v0.1","problem":221,"statement":"Is there a set $A\\subset\\mathbb{N}$ such that, for all large $N$,\\[\\lvert A\\cap\\{1,\\ldots,N\\}\\rvert \\ll N/\\log N\\]and such that every large integer can be written as $2^k+a$ for some $k\\geq 0$ and $a\\in A$?","status":"solved","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)"}