{"schema":"vela.problem-packet.v0.1","problem":696,"statement":"Let $h(n)$ be the largest $\\ell$ such that there is a sequence of primes $p_1<\\cdots < p_\\ell$ all dividing $n$ with $p_{i+1}\\equiv 1\\pmod{p_i}$. Let $H(n)$ be the largest $u$ such that there is a sequence of integers $d_1<\\cdots < d_u$ all dividing $n$ with $d_{i+1}\\equiv 1\\pmod{d_i}$.Estimate $h(n)$ and $H(n)$. Is it true that $H(n)/h(n)\\to \\infty$ for almost all $n$?","status":"solved","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}