{"schema":"vela.problem-packet.v0.1","problem":864,"statement":"Let $A\\subseteq \\{1,\\ldots N\\}$ be a set such that there exists at most one $n$ with more than one solution to $n=a+b$ (with $a\\leq b\\in A$). Estimate the maximal possible size of $\\lvert A\\rvert$ - in particular, is it true that\\[\\lvert A\\rvert \\leq (1+o(1))\\frac{2}{\\sqrt{3}}N^{1/2}?\\]","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A389182","name":"Maximum cardinality of a subset of {1,...,n} in which all sums a+b of elements a<=b are distinct except possibly one.","terms":"1,2,3,3,4,4,5,5,5,5,6,6,6,6,7,7,7,7,7,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,11,12,12,","url":"https://oeis.org/A389182"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}