{"schema":"vela.problem-packet.v0.1","problem":169,"statement":"Let $k\\geq 3$ and $f(k)$ be the supremum of $\\sum_{n\\in A}\\frac{1}{n}$ as $A$ ranges over all sets of positive integers which do not contain a $k$-term arithmetic progression. Estimate $f(k)$. Is\\[\\lim_{k\\to \\infty}\\frac{f(k)}{\\log W(k)}=\\infty\\]where $W(k)$ is the van der Waerden number?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A005346","name":"Van der Waerden numbers W(2,n).","terms":"1,3,9,35,178,1132","url":"https://oeis.org/A005346"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}