{"schema":"vela.problem-packet.v0.1","problem":1026,"statement":"Let $x_1,\\ldots,x_n$ be a sequence of distinct real numbers. Determine\\[\\max\\left(\\sum x_{i_r}\\right),\\]where the maximum is taken over all monotonic subsequences.","status":"solved","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A391431","name":"Numerator of k + a/k where n = k^2 + 2*a + 1 and -k <= a <= k.","terms":"1,1,3,2,2,7,5,8,3,3,13,10,7,11,15,4,4,21,17,22,9,23,19,24,5,5,31,26,16,27,11,28,17,29,35,6,6,43,37,44,19,45,13,46,20,47,","url":"https://oeis.org/A391431"},{"id":"A391490","name":"Denominator of k + a/k where n = k^2 + 2a + 1 and -k <= a <= k.","terms":"1,1,2,1,1,3,2,3,1,1,4,3,2,3,4,1,1,5,4,5,2,5,4,5,1,1,6,5,3,5,2,5,3,5,6,1,1,7,6,7,3,7,2,7,3,7,6,7,1,1,8,7,4,7,8,7,2,7,8,7,","url":"https://oeis.org/A391490"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}