DouKaku?

static void Main(string[] args)
{
  for (int n = 1; n < 200; n++)
  {
    decimal f = Func(n);
    if (IsAlmostInteger(f, 4))
      Console.WriteLine("{0} {1:f6}", n, f);
  }
  Console.ReadKey();
}

static decimal Func(int i)
{
  return DecimalExpQuick(3.141592653589793238462643383279M * DecimalSqrt((decimal)i));
}

static decimal DecimalExpQuick(decimal d)
{
  int n = 0;
  decimal p = 1.0M;
  decimal t = d;
  do
  {
    n++;
    p *= 2;
    t /= 2;
  }
  while (t >= 0.1M);

  decimal et = DecimalExp(t);
  decimal ex = 1;
  for(int i = 0; i < p; i++)
    ex *= et;
  return ex;
}

static decimal DecimalExp(decimal t)
{
  int i = 0;
  decimal et = 0.0M;
  decimal ai = 1.0M;
  do
  {
    et += ai;
    i++;
    ai = ai * (t / i);
  }
  while (!NearlyEquals(ai, 0.0M));
  return et;
}

static decimal DecimalSqrt(decimal d)
{
  decimal x = 1.0M;
  decimal betterX = 0.0M;
  while(true)
  {
    betterX = SqrtBailey(x, d);
    if (NearlyEquals(x, betterX))
      return betterX;
    x = betterX;
  }
}

static decimal SqrtBailey(decimal x, decimal d)
{
  decimal fx = x * x - d;
  decimal dfx = 2.0M * x;
  return x - (fx / (dfx - (fx / dfx)));
}

static bool NearlyEquals(decimal d1, decimal d2)
{
  int dights = IntDight(d1);
  decimal delta = 1e-28M * (decimal)Math.Pow(10, dights);
  return ((d1 - d2 < delta) && (d2 - d1 < delta));
}

static int IntDight(decimal d)
{
  if (d < decimal.Zero)
    d = decimal.Negate(d);
  return IntAbsDight(d);
}

static int IntAbsDight(decimal d)
{
  int i = 0;
  while (d >= decimal.One)
  {
    d /= 10.0M;
    i++;
  }
  return i;
}

static bool IsAlmostInteger(decimal d, int dights)
{
  decimal p = (decimal)Math.Pow(10, dights);
  decimal d1 = decimal.Round(d) * p;
  decimal d2 = decimal.Round(d * p);
  return ((d1 - d2 <= 1.0M) && (d2 - d1 <= 1.0M));
}