{"schema":"vela.problem-packet.v0.1","problem":186,"statement":"Let $F(N)$ be the maximal size of $A\\subseteq \\{1,\\ldots,N\\}$ which is 'non-averaging', so that no $n\\in A$ is the arithmetic mean of at least two elements in $A$. What is the order of growth of $F(N)$?","status":"solved","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A389784","name":"a(n) is the maximum size of a subset A of {1,...,n} such that no element in A is the average of a subset of A with cardinality at least 2.","terms":"1,2,2,3,4,4,4,4,4,5,6,6,6,6,6,7,7,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,1","url":"https://oeis.org/A389784"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}