{"schema":"vela.problem-packet.v0.1","problem":854,"statement":"Let $n_k$ denote the $k$th primorial, i.e. the product of the first $k$ primes.If $1=a_1<a_2<\\cdots a_{\\phi(n_k)}=n_k-1$ is the sequence of integers coprime to $n_k$, then estimate the smallest even integer not of the form $a_{i+1}-a_i$. Are there\\[\\gg \\max_i (a_{i+1}-a_i)\\]many even integers of the form $a_{j+1}-a_j$?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A048670","name":"Jacobsthal function A048669 applied to the product of the first n primes (A002110).","terms":"2,4,6,10,14,22,26,34,40,46,58,66,74,90,100,106,118,132,152,174,190,200,216,234,258,264,282,300,312,330,354,378,388,414,4","url":"https://oeis.org/A048670"},{"id":"A389839","name":"Smallest even number which cannot be written as the difference of two consecutive numbers which are relatively prime to the primorial prime(n)#.","terms":"6,8,12,16,20,28,32,42,48,60,68","url":"https://oeis.org/A389839"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}