P6124 [NEERC 2015] Binary vs Decimal
Description
A positive number $A$ is considered valid if it contains only `0` or `1`, and after converting it to binary as $B$, $A$ is a suffix of $B$.
Now you are given a number $N$. Find the $N$-th such number.
Input Format
One line with one number $N$.
Output Format
One line with one number: the $N$-th number.
Explanation/Hint
$1 \le N \le 10^4$.
|Original|Binary|Comment|
| :-----------: | :-----------: | :-----------: |
|$1$|$1$|√|
|$10$|$1010$|√|
|$11$|$1011$|√|
|$100$|$1100100$|√|
|$101$|$1100101$|√|
|$110$|$1101110$|√|
|$111$|$1101111$|√|
|$1000$|$1111101000$|√|
|$1001$|$1111101001$|√|
|$1010$|$1111110010$|×|
|$1011$|$1111110011$|×|
|$1100$|$10001001100$|√|
Translated by ChatGPT 5