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Comments on Partial Sums of Harmonic Series

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Partial Sums of Harmonic Series

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Given an positive integer $n$, return the least positive integer $k$ such that the $k$th partial sum of the harmonic series is greater than or equal to $n$. For example, if $n = 2$, then $k = 4$, because $1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} = \frac{25}{12} > 2$.

More Input/Output Examples

Input -> Output
1 -> 1
3 -> 11
4 -> 31

This is code-golf, so shortest code wins.

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+5
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AppleScript, 178 bytes

set n to text returned of (display dialog "" default answer "") as number
set k to 0
set h to 0
repeat
set k to k + 1
set h to h + (1 / k)
if h >= n then exit repeat
end repeat
k

It's really a shame that AppleScript doesn't support explicit stdin.

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