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erdős #290

← #289 · #291 → (packet.json; erdosproblems.com)

Let $a \geq 1$ . Must there exist some $b > a$ such that $a \leq n \leq b \sum \frac{1}{n} = \frac{r _{1}}{s _{1}} and a \leq n \leq b + 1 \sum \frac{1}{n} = \frac{r _{2}}{s _{2}},$ with $(r_{i}, s_{i}) = 1$ and $s_{2} < s_{1}$ ? If so, how does this $b (a)$ grow with $a$ ?

Worked, still open.

number theory · solved · 0 attempts

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A375081 — 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).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,

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finding.noted · reviewer:will-blair · 1 day

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