Task

Show that the following remarkable formula gives the sequence of non-square natural numbers:

            n + floor(1/2 + sqrt(n)) 

 Print out the values for    n    in the range   1   to   22
 Show that no squares occur for    n    less than one million


This is sequence   A000037   in the OEIS database.




using System;
using System.Diagnostics;
 
namespace sons
{
    class Program
    {
        static void Main(string[] args)
        {
            for (int i = 1; i < 23; i++)            
                Console.WriteLine(nonsqr(i));            
 
            for (int i = 1; i < 1000000; i++)
            {
                double j = Math.Sqrt(nonsqr(i));
                Debug.Assert(j != Math.Floor(j),"Square");
            }            
        }
 
        static int nonsqr(int i)
        {
            return (int)(i + Math.Floor(0.5 + Math.Sqrt(i)));
        }
    }
}