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Comments on Partial Sums of Harmonic Series

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Partial Sums of Harmonic Series

+12
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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.

code-golf
posted about 4 years ago
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Quintec‭
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Japt, 11 10 bytes 

>0©ÒßUÉ/°T

Try it

>0©ÒßUÉ/°T     :Implicit input of integer U
>0             :Greater than 0?
  ©            :Logical AND with
   Ò           :Negate the bitwise NOT of (i.e., increment)
    ß          :Recursive call with argument
     UÉ/       :  U minus 1 divided by ...
        °T     :  T (initially 0) prefix incremented
posted about 4 years ago
3y ago
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Shaggy‭
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General comments (3 comments)
General comments
Quintec‭ wrote about 4 years ago
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Out of curiosity, I've seen this in a few of your other answers now (using shortcuts instead of one character alternatives) - why Ä at the end instead of 1?

Shaggy‭ wrote about 4 years ago
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Sometimes it's a hangover from a previous attempt at a solution, @Quintec, other times it's me trying to keep various tricks fresh in my mind and, occasionally, it's just to show off!

Shaggy‭ wrote over 3 years ago · edited over 3 years ago
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@Quintec, for the sake of simplifying the explanation, the Ä is now gone.