// Note that T(1 + 2k) = H(1 + k), so every HexagonalNumber is a TriangleNumber
// Proof: T(1 + 2k) = (1 + 2k)*(1 + 2k + 1) / 2 = (1 + 2k)*(1 + k),
// and H(n + k) = (1 + k)*(2(1 + k) - 1) = (1 + k)*(1 + 2k)
public static List <long> GetFirstNTriangleNumbersWhichAreAlsoPentagonalAndHexogonal(int count)
{
var listOfNumbersFound = new List <long>();
long n = 1;
while (count != 0)
{
var nthTriangleNumber = GetNthTriangleNumber(n);
if (PentagonNumberHelper.IsPentagonalNumber(nthTriangleNumber))
{
listOfNumbersFound.Add(nthTriangleNumber);
count--;
}
n += 2;
}
return(listOfNumbersFound);
}
public static long GetSolutionOfProblem44()
{
return(PentagonNumberHelper.GetMinimalDistanceOfPentagonalNumbersForWhichSumAndDifferenceArePentagonal());
}