{"schema":"vela.problem-packet.v0.1","problem":472,"statement":"Given some initial finite sequence of primes $q_1<\\cdots<q_m$ extend it so that $q_{n+1}$ is the smallest prime of the form $q_n+q_i-1$ for $n\\geq m$. Is there an initial starting sequence so that the resulting sequence is infinite?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A389713","name":"a(1) = 3, a(2) = 5, a(n) is the smallest prime such that a(n) - a(n-1) + 1 is in the sequence.","terms":"3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,101,103,107,109,113,131,137,139,149,151,157,163,167,17","url":"https://oeis.org/A389713"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}