{"schema":"vela.problem-packet.v0.1","problem":271,"statement":"Let $A(n)=\\{a_0<a_1<\\cdots\\}$ be the sequence defined by $a_0=0$ and $a_1=n$, and for $k\\geq 1$ define $a_{k+1}$ as the least positive integer such that there is no three-term arithmetic progression in $\\{a_0,\\ldots,a_{k+1}\\}$.Can the $a_k$ be explicitly determined? How fast do they grow?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A005487","name":"Starts 0, 4 and contains no 3-term arithmetic progression.","terms":"0,4,5,7,11,12,16,23,26,31,33,37,38,44,49,56,73,78,80,85,95,99,106,124,128,131,136,143,169,188,197,203,220,221,226,227,23","url":"https://oeis.org/A005487"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}