/*

  Consider a monotonic sequence of natural numbers

  where each number k occurs k times: 1, 2, 2, 3, 3, 3, 4, 4, 4, 4 etc.

  Write a program that inputs integer n>0 and prints n-th element of this sequence. 

*/                  

using System;

using System.Diagnostics;

public class Program

{

    public static int InputInt(string prompt)

    {

        Console.Write("Enter " + prompt + ": ");

        return Convert.ToInt32(Console.ReadLine());

    }

​

    public static void Main()

    {

        int n = InputInt("n");

        Trace.Assert(n > 0);

        // Inductive extension:

        int i       = 1;    // index of the last element i>0

        int last    = 1;    // last element of the sequence

        int count   = 1;    // number of times the last element occurs 

        // invariant: inductive extension definition and i<=n

        while(i != n)

        {

            i++;

            if(last==count)

            {

                last = count + 1;

                count = 1;

            }

            else

            {

                count++;

            }

        }

        // i==n => last==n-th element

        Console.WriteLine("{0}-th element is {1}", n, last);

    }

}