# Program to find the Nth natural number with exactly two bits set

Given an integer **N**, the task is to find the **Nth** natural number with exactly two bits set. **Examples:**

Input:N = 4Output:9Explanation:

Numbers with exactly two bits set: 3, 5, 6, 9, 10, 12, …

4th number in this is 9Input:N = 15Output:48

**Naive Approach:**

- Run a loop through all natural numbers, and for each number, check if it has two bits set or not by counting set bits in a number.
- Print the Nth number having two set bits.

**Efficient Approach: **

- Find the leftmost set bit by finding the partition to which N belongs (Partition ‘i’ has ‘i’ numbers in it).
- To find the other set bit, we’ll have to first find the distance of N from the last number of the previous partition. Based on their difference, we set the corresponding bit.

k = k | (1<<(i))

**Below is the implementation of the above approach:**

## C++

`// C++ Code to find the Nth number` `// with exactly two bits set` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to find the Nth number` `// with exactly two bits set` `void` `findNthNum(` `long` `long` `int` `N)` `{` ` ` `long` `long` `int` `bit_L = 1, last_num = 0;` ` ` `// Keep incrementing until` ` ` `// we reach the partition of 'N'` ` ` `// stored in bit_L` ` ` `while` `(bit_L * (bit_L + 1) / 2 < N) {` ` ` `last_num = last_num + bit_L;` ` ` `bit_L++;` ` ` `}` ` ` `// set the rightmost bit` ` ` `// based on bit_R` ` ` `int` `bit_R = N - last_num - 1;` ` ` `cout << (1 << bit_L) + (1 << bit_R)` ` ` `<< endl;` `}` `// Driver code` `int` `main()` `{` ` ` `long` `long` `int` `N = 13;` ` ` `findNthNum(N);` ` ` `return` `0;` `}` |

## Java

`// Java Code to find the Nth number` `// with exactly two bits set` `class` `GFG{` ` ` `// Function to find the Nth number` `// with exactly two bits set` `static` `void` `findNthNum(` `int` `N)` `{` ` ` ` ` `int` `bit_L = ` `1` `, last_num = ` `0` `;` ` ` ` ` `// Keep incrementing until` ` ` `// we reach the partition of 'N'` ` ` `// stored in bit_L` ` ` `while` `(bit_L * (bit_L + ` `1` `) / ` `2` `< N) {` ` ` `last_num = last_num + bit_L;` ` ` `bit_L++;` ` ` `}` ` ` ` ` `// set the rightmost bit` ` ` `// based on bit_R` ` ` `int` `bit_R = N - last_num - ` `1` `;` ` ` ` ` `System.out.print((` `1` `<< bit_L) + (` `1` `<< bit_R)` ` ` `+` `"\n"` `);` `}` ` ` `// Driver code` `public` `static` `void` `main(String[] args)` `{` ` ` `int` `N = ` `13` `;` ` ` ` ` `findNthNum(N);` `}` `}` `// This code is contributed by Princi Singh` |

## Python3

`# Python Code to find the Nth number` `# with exactly two bits set` `# Function to find the Nth number` `# with exactly two bits set` `def` `findNthNum(N):` ` ` `bit_L ` `=` `1` `;` ` ` `last_num ` `=` `0` `;` ` ` `# Keep incrementing until` ` ` `# we reach the partition of 'N'` ` ` `# stored in bit_L` ` ` `while` `(bit_L ` `*` `(bit_L ` `+` `1` `) ` `/` `2` `< N):` ` ` `last_num ` `=` `last_num ` `+` `bit_L;` ` ` `bit_L` `+` `=` `1` `;` ` ` ` ` `# set the rightmost bit` ` ` `# based on bit_R` ` ` `bit_R ` `=` `N ` `-` `last_num ` `-` `1` `;` ` ` `print` `((` `1` `<< bit_L) ` `+` `(` `1` `<< bit_R));` `# Driver code` `if` `__name__ ` `=` `=` `'__main__'` `:` ` ` `N ` `=` `13` `;` ` ` `findNthNum(N);` `# This code contributed by PrinciRaj1992` |

## C#

`// C# Code to find the Nth number` `// with exactly two bits set` `using` `System;` `class` `GFG{` ` ` `// Function to find the Nth number` `// with exactly two bits set` `static` `void` `findNthNum(` `int` `N)` `{` ` ` ` ` `int` `bit_L = 1, last_num = 0;` ` ` ` ` `// Keep incrementing until` ` ` `// we reach the partition of 'N'` ` ` `// stored in bit_L` ` ` `while` `(bit_L * (bit_L + 1) / 2 < N) {` ` ` `last_num = last_num + bit_L;` ` ` `bit_L++;` ` ` `}` ` ` ` ` `// set the rightmost bit` ` ` `// based on bit_R` ` ` `int` `bit_R = N - last_num - 1;` ` ` ` ` `Console.Write((1 << bit_L) + (1 << bit_R)` ` ` `+` `"\n"` `);` `}` ` ` `// Driver code` `public` `static` `void` `Main(String[] args)` `{` ` ` `int` `N = 13;` ` ` ` ` `findNthNum(N);` `}` `}` `// This code is contributed by Princi Singh` |

## Javascript

`<script>` `// JavaScript Code to find the Nth number` `// with exactly two bits set` `// Function to find the Nth number` `// with exactly two bits set` `function` `findNthNum(N)` `{` ` ` `let bit_L = 1, last_num = 0;` ` ` `// Keep incrementing until` ` ` `// we reach the partition of 'N'` ` ` `// stored in bit_L` ` ` `while` `(bit_L * (bit_L + 1) / 2 < N) {` ` ` `last_num = last_num + bit_L;` ` ` `bit_L++;` ` ` `}` ` ` `// set the rightmost bit` ` ` `// based on bit_R` ` ` `let bit_R = N - last_num - 1;` ` ` `document.write((1 << bit_L) + (1 << bit_R)` ` ` `+ ` `"<br>"` `);` `}` `// Driver code` `let N = 13;` `findNthNum(N);` `// This code is contributed by Mayank Tyagi` `</script>` |

**Output:**

36

**Time Complexity : **O(Partition of Number)

**Auxiliary space:** O(1) as it is using constant variables