{"schema":"vela.problem-packet.v0.1","problem":295,"statement":"Let $N\\geq 1$ and let $k(N)$ denote the smallest $k$ such that there exist $N\\leq n_1&#60;\\cdots &#60;n_k$ with\\[1=\\frac{1}{n_1}+\\cdots+\\frac{1}{n_k}.\\]Is it true that\\[\\lim_{N\\to \\infty} k(N)-(e-1)N=\\infty?\\]","status":"open","seam":"sealed","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[{"id":"att_75210637be1c42c5","kind":"transfer","claim":"Transfer from #306: exact k(N) (min unit fractions summing to 1 with all denominators >=N) for N=1..11 = [1,3,5,8,10,11,13,15,17,19,21] (Opus-verified); PROVED k(N) finite for every N; frontier 22<k(12)<=24.","grade":"verified_reduction","gateStatus":"needs_verification","superseded":false}],"velaLean":[],"oeis":[{"id":"A192881","name":"Number of terms for the shortest Egyptian fraction representation of 1 starting with 1/n.","terms":"1,3,5,8,10,11,13,15,17,19,21,23,25,26,28,30","url":"https://oeis.org/A192881"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}