{"schema":"vela.problem-packet.v0.1","problem":954,"statement":"Let $0=a_0&#60;a_1&#60;a_2&#60;\\cdots$ be the sequence of integers defined by $a_0=0$ and $a_1=1$, and $a_{k+1}$ is the smallest integer $n$ for which the number of solutions to $a_i+a_j \\leq n$ (with $0\\leq i\\leq j\\leq k$ and $j\\geq 1$) is $&#60;n$.Is the number of solutions to $a_i+a_j \\leq x$ equal to $x+O(x^{1/4+o(1)})$?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A390642","name":"a(n) is the smallest integer k such that the number of sums a(i) + a(j) <= k for i <= j < n is less than k - n + 1.","terms":"1,3,5,9,13,17,24,31,38,45,53,61,75,87,97,112,124,139,147,175,182,205,219,242,265,277,309,313,349,378,386,430,445,478,480","url":"https://oeis.org/A390642"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}