{"schema":"vela.problem-packet.v0.1","problem":424,"statement":"Let $a_1=2$ and $a_2=3$ and continue the sequence by appending to $a_1,\\ldots,a_n$ all possible values of $a_ia_j-1$ with $i\\neq j$. Is it true that the set of integers which eventually appear has positive density?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A005244","name":"A self-generating sequence: start with 2 and 3, take all products of any 2 previous elements, subtract 1 and adjoin them to the sequence.","terms":"2,3,5,9,14,17,26,27,33,41,44,50,51,53,65,69,77,80,81,84,87,98,99,101,105,122,125,129,131,134,137,149,152,153,158,159,161","url":"https://oeis.org/A005244"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}