{"schema":"vela.problem-packet.v0.1","problem":860,"statement":"Let $h(n)$ be such that, for any $m\\geq 1$, in the interval $(m,m+h(n))$ there exist distinct integers $a_i$ for $1\\leq i\\leq \\pi(n)$ such that $p_i\\mid a_i$, where $p_i$ denotes the $i$th prime. Estimate $h(n)$.","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)"}