{"schema":"vela.problem-packet.v0.1","problem":781,"statement":"Let $f(k)$ be the minimal $n$ such that any $2$-colouring of $\\{1,\\ldots,n\\}$ contains a monochromatic $k$-term descending wave: a sequence $x_1<\\cdots <x_k$ such that, for $1<j<k$,\\[x_j \\geq \\frac{x_{j+1}+x_{j-1}}{2}.\\]Estimate $f(k)$. In particular is it true that $f(k)=k^2-k+1$ for all $k$?","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)"}