{"schema":"vela.problem-packet.v0.1","problem":687,"statement":"Let $Y(x)$ be the maximal $y$ such that there exists a choice of congruence classes $a_p$ for all primes $p\\leq x$ such that every integer in $[1,y]$ is congruent to at least one of the $a_p\\pmod{p}$. Give good estimates for $Y(x)$. In particular, can one prove that $Y(x)=o(x^2)$ or even $Y(x)\\ll x^{1+o(1)}$?","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":"A058989","name":"Largest number of consecutive integers such that each is divisible by a prime <= the n-th prime.","terms":"1,3,5,9,13,21,25,33,39,45,57,65,73,89,99,105,117,131,151,173,189,199,215,233,257,263,281,299,311,329,353,377,387,413,431","url":"https://oeis.org/A058989"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}