{"schema":"vela.problem-packet.v0.1","problem":241,"statement":"Let $f(N)$ be the maximum size of $A\\subseteq \\{1,\\ldots,N\\}$ such that the sums $a+b+c$ with $a,b,c\\in A$ are all distinct (aside from the trivial coincidences). Is it true that\\[ f(N)\\sim N^{1/3}?\\]","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A387704","name":"Size of the maximal subset S of {1,2,...,n} such that for all a, b, c in S not necessarily distinct, a+b+c is unique up to permutation.","terms":"0,1,2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,","url":"https://oeis.org/A387704"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}