第N个礼貌数字

礼貌数字是一个正整数，可以写为两个或多个连续的正整数之和。给定N，找到第N个礼貌数字。
例子：

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.

存在一个有趣的模式，即礼让数字系列中不存在2的幂。基于这个事实，存在第N个礼貌数的以下公式(Lambek–Moser定理)。
$f(n) = n+ \left \lfloor log_2 (n+ log_2 n) \right \rfloor$
在这里要找到第N个礼貌数字，我们必须在上式中将n取为n + 1
内置的日志函数计算log base-e，因此将其除以log base-e 2将得到log base-2的值。
下面给出的是上述方法的实现：

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

Javascript

 
// Javascript program to find
// Nth polite number
 
// function to evaluate
// Nth polite number
function polite(n)
{
    n += 1;
    let base = 2;
    return n + (Math.log((n + (Math.log(n) /
                Math.log(base))))) / Math.log(base);
}
 
// Driver code
n = 7;
document.write(parseInt(polite(n)));
 
// This code is contributed by _saurabh_jaiswal.
 

输出：

11

参考：维基百科