(C#) Project Euler 045 - Triangular, Pentagonal, Hexagonal

// Triangle, pentagonal, and hexagonal numbers are generated by the following formulae:

// Triangle     Tn = n(n+1)/2   1, 3, 6, 10, 15, ...
// Pentagonal   Pn = n(3n-1)/2  1, 5, 12, 22, 35, ...
// Hexagonal    Hn = n(2n-1)    1, 6, 15, 28, 45, ...

// It can be verified that T285 = P165 = H143 = 40755.

// Find the next triangle number that is also pentagonal and hexagonal.

 

 

 

using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Numerics;

namespace practice
{
    class Program
    {
        static void Main(string[] args)
        {
            List<long> triangles = GetTriangles();

            long n = 40756;

            for(int i = 287; i < triangles.Count; i++){
                long k = triangles[i];
                if(CheckPentagonal(k) && CheckHexagonal(k)){
                    n = k;
                    break;
                }
            }

            Console.Write(n);
        }

        static List<long> GetTriangles()
        {
            List<long> triangles = new List<long>();

            for (long i = 1; i < 10000000; i++)
            {
                long t = (i * (i + 1)) / 2;
                triangles.Add(t);
            }

            return triangles;
        }

        static bool CheckPentagonal(long k)
        {
            double n = (Math.Sqrt(24 * k + 1) + 1) / 6;
            return n == (long)n;
        }

        static bool CheckHexagonal(long k)
        {
            double n = (Math.Sqrt(8 * k + 1) + 1) / 4;
            return n == (long)n;
        }
    }
}