{"schema":"vela.problem-packet.v0.1","problem":695,"statement":"Let $p_1<p_2<\\cdots$ be a sequence of primes such that $p_{i+1}\\equiv 1\\pmod{p_i}$. Is it true that\\[\\lim_k p_k^{1/k}=\\infty?\\]Does there exist such a sequence with\\[p_k \\leq \\exp(k(\\log k)^{1+o(1)})?\\]","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A061092","name":"a(0) = 1; for n>0, a(n) = smallest prime of the form k*a(n-1) + 1.","terms":"1,2,3,7,29,59,709,2837,22697,590123,1180247,9441977,169955587,2719289393,5438578787,32631472723,391577672677,15663106907","url":"https://oeis.org/A061092"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}