{"schema":"vela.problem-packet.v0.1","problem":243,"statement":"Let $1\\leq a_1<a_2<\\cdots$ be a sequence of integers such that\\[\\lim_{n\\to \\infty}\\frac{a_n}{a_{n-1}^2}=1\\]and $\\sum\\frac{1}{a_n}\\in \\mathbb{Q}$. Then, for all sufficiently large $n\\geq 1$,\\[ a_n = a_{n-1}^2-a_{n-1}+1.\\]","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A000058","name":"Sylvester's sequence: a(n+1) = a(n)^2 - a(n) + 1, with a(0) = 2.","terms":"2,3,7,43,1807,3263443,10650056950807,113423713055421844361000443,12864938683278671740537145998360961546653259485195807","url":"https://oeis.org/A000058"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}