{"schema":"vela.problem-packet.v0.1","problem":107,"statement":"Let $f(n)$ be minimal such that any $f(n)$ points in $\\mathbb{R}^2$, no three on a line, contain $n$ points which form the vertices of a convex $n$-gon. Prove that $f(n)=2^{n-2}+1$.","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A000051","name":"a(n) = 2^n + 1.","terms":"2,3,5,9,17,33,65,129,257,513,1025,2049,4097,8193,16385,32769,65537,131073,262145,524289,1048577,2097153,4194305,8388609,","url":"https://oeis.org/A000051"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}