N-th polite number in C++

A polite number is a positive number that can be written as the sum of 2 or more consecutive positive numbers.

The series of polite numbers are

3 5 6 7 9 10 11 12 13 14...

There exists a formula to find the n-th polite number. The formula is n + log2(n + log2(n)). The default log computes with base e. We need to compute using base 2. Divide the default log result with log(2) to get the value of log with base e.


  • Algorithm to the n-th polite number is straightforward.
  • Initialise the number N.
  • Use the above formula to compute the n-th polite number.
  • Make sure to increment the value of n by 1 before computing the n-th polite number.


Following is the implementation of the above algorithm in C++

#include <bits/stdc++.h>
using namespace std;
double getNthPoliteNumber(double n) {
   n += 1;
   return n + (log((n + (log(n) / log(2.0))))) / log(2.0);
int main() {
   double n = 10;
   cout << (int)getNthPoliteNumber(n) << endl;
   return 0;


If you run the above code, then you will get the following result.