{"schema":"vela.problem-packet.v0.1","problem":125,"statement":"Let $A = \\{ \\sum\\epsilon_k3^k : \\epsilon_k\\in \\{0,1\\}\\}$ be the set of integers which have only the digits $0,1$ when written base $3$, and $B=\\{ \\sum\\epsilon_k4^k : \\epsilon_k\\in \\{0,1\\}\\}$ be the set of integers which have only the digits $0,1$ when written base $4$. Does $A+B$ have positive lower density?","status":"solved","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[{"verdict":"variant","attestedBy":"reviewer:will-blair","formalRef":"erdos_125.variants.positive_lower_density.lean","targetFinding":"vf_63cf7f09150f3200"}],"attempts":[],"velaLean":[],"oeis":[{"id":"A367090","name":"Numbers that cannot be written as a sum of distinct powers of 3 and distinct powers of 4.","terms":"62,63,143,144,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,23","url":"https://oeis.org/A367090"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}