{"schema":"vela.problem-packet.v0.1","problem":1134,"statement":"Let $A\\subseteq \\mathbb{N}$ be the smallest set which contains $1$ and is closed under the operations\\[x\\mapsto 2x+1,\\]\\[x\\mapsto 3x+1,\\]and\\[x\\mapsto 6x+1.\\]Does $A$ have positive lower density?","status":"solved","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A185661","name":"Smallest set containing 1 and closed under the operations x->2x+1, x->3x+1, x->6x+1.","terms":"1,3,4,7,9,10,13,15,19,21,22,25,27,28,31,39,40,43,45,46,51,55,57,58,61,63,64,67,76,79,81,82,85,87,91,93,94,103,111,115,11","url":"https://oeis.org/A185661"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}