{"schema":"vela.problem-packet.v0.1","problem":206,"statement":"Let $x>0$ be a real number. For any $n\\geq 1$ let\\[R_n(x) = \\sum_{i=1}^n\\frac{1}{m_i}<x\\]be the maximal sum of $n$ distinct unit fractions which is $<x$.Is it true that, for almost all $x$, for sufficiently large $n$, we have\\[R_{n+1}(x)=R_n(x)+\\frac{1}{m},\\]where $m$ is minimal such that $m$ does not appear in $R_n(x)$ and the right-hand side is $<x$? (That is, are the best underapproximations eventually always constructed in a 'greedy' fashion?)","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)"}