{"schema":"vela.problem-packet.v0.1","problem":290,"statement":"Let $a\\geq 1$. Must there exist some $b>a$ such that\\[\\sum_{a\\leq n\\leq b}\\frac{1}{n}=\\frac{r_1}{s_1}\\textrm{ and }\\sum_{a\\leq n\\leq b+1}\\frac{1}{n}=\\frac{r_2}{s_2},\\]with $(r_i,s_i)=1$ and $s_2<s_1$? If so, how does this $b(a)$ grow with $a$?","status":"solved","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A375081","name":"Smallest k>n such that the denominator of Sum {i=n..k} (1/i) is larger than the denominator of Sum {i=n..k+1} (1/i).","terms":"5,5,5,17,17,14,14,14,14,14,32,34,34,34,27,27,27,27,23,23,27,51,51,51,51,44,44,44,44,44,39,39,39,39,39,44,74,74,74,74,74,","url":"https://oeis.org/A375081"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}