{"schema":"vela.problem-packet.v0.1","problem":1030,"statement":"Let $R(k,l)$ be the usual Ramsey number: the smallest $n$ such that if the edges of $K_n$ are coloured red and blue then there exists either a red $K_k$ or a blue $K_l$.Prove the existence of some $c>0$ such that\\[\\lim_{k\\to \\infty}\\frac{R(k+1,k)}{R(k,k)}> 1+c.\\]","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A000791","name":"Ramsey numbers R(3,n).","terms":"1,3,6,9,14,18,23,28,36","url":"https://oeis.org/A000791"},{"id":"A059442","name":"Array of Ramsey numbers R(n,k) (n >= 2, k >= 2) read by antidiagonals.","terms":"2,3,3,4,6,4,5,9,9,5,6,14,18,14,6,7,18,25,25,18,7,8,23","url":"https://oeis.org/A059442"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}