{"schema":"vela.problem-packet.v0.1","problem":454,"statement":"Let\\[f(n) = \\min_{i&#60;n} (p_{n+i}+p_{n-i}),\\]where $p_k$ is the $k$th prime. Is it true that\\[\\limsup_n (f(n)-2p_n)=\\infty?\\]","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A389676","name":"a(n) = Min_{0<i<n} (prime(n-i) + prime(n+i)).","terms":"7,10,16,20,26,32,40,48,54,62,70,78,88,96,104,114,120,130,140,150,156,166,174,182,192,202,212,220,236,244,252,264,276,286","url":"https://oeis.org/A389676"},{"id":"A389677","name":"a(n) = A389676(n) - 2*prime(n).","terms":"1,0,2,-2,0,-2,2,2,-4,0,-4,-4,2,2,-2,-4,-2,-4,-2,4,-2,0,-4,-12,-10,-4,-2,2,10,-10,-10,-10,-2,-12,-8,-8,-14,-4,-8,-8,0,-10","url":"https://oeis.org/A389677"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}