# N-th polite number

A polite number is a positive integer that can be written as the sum of two or more consecutive positive integers. Given N, find the N-th polite number.

Examples:

Input : 4
Output : 7
Explanation: The first 3 are 3(1+2), 5(2+3),
6(1+2+3).

Input : 7
Output : 11
Explanation:  3, 5, 6, 7, 9, 10, 11.


## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

There exist an interesting pattern that only powers of 2 are not present in series of Polite numbers. Based on this fact, there exist below formula (Lambek–Moser theorem) for N-th polite number. Here to find Nth polite number we have to take n as n+1 in the above equation

The inbuilt log function computes log base-e, so dividing it by log base-e 2 will give log base-2 value.

Given below is the implementation of the above approach:

## C++

 // CPP program to find Nth polite number  #include  using namespace std;     // function to evaluate Nth polite number  double polite(double n)  {      n += 1;      double base = 2;      return n + (log((n + (log(n) /                   log(base))))) / log(base);  }     // driver code  int main()  {      double n = 7;         cout << (int)polite(n);      return 0;  }

## Java

 // Java program for finding N-th polite number  import java.io.*;     class GFG {         // function to find N-th polite number      static double polite(double n)      {          n += 1;          double base = 2;          return n + (Math.log((n + (Math.log(n) /                  Math.log(base))))) / Math.log(base);      }         // driver code      public static void main(String[] args)      {          double n = 7;          System.out.println((int)polite(n));      }  }

## Python

 import math  # function to find Nth polite number   def Polite(n):      n = n + 1     return (int)(n+(math.log((n + math.log(n, 2)), 2)))      # Driver code  n = 7 print Polite(n)

## C#

 // Java program for finding   // N-th polite number  using System;     class GFG {         // Function to find N-th polite number      static double polite(double n)      {          n += 1;          double base1 = 2;          return n + (Math.Log((n + (Math.Log(n) /                        Math.Log(base1))))) /                        Math.Log(base1);      }         // Driver code      public static void Main(String []args)      {          double n = 7;          Console.Write((int)polite(n));      }  }     // This code is contributed by  // Smitha Dinesh Semwal

## PHP

 

Output:

11


Reference: Wikipedia

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