{"schema":"vela.problem-packet.v0.1","problem":435,"statement":"Let $n\\in\\mathbb{N}$ with $n\\neq p^k$ for any prime $p$ and $k\\geq 0$. What is the largest integer not of the form\\[\\sum_{1\\leq i<n}c_i\\binom{n}{i}\\]where the $c_i\\geq 0$ are integers?","status":"solved","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A389479","name":"a(n) is the Frobenius number for the set { binomial(m,k), k=1..m-1 } where m = A024619(n).","terms":"49,1043,989,20669,12907,99007,67031,700319,7054529,750397,124807499,7125065,578549,1935378079,37337700047,41645613,18836","url":"https://oeis.org/A389479"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}