Project Euler NO45

三角數，五角數和六角數分別通過以下公式定義：

三角數		Tn=n(n+1)/2		1, 3, 6, 10, 15, ...
五角數		Pn=n(3n1)/2		1, 5, 12, 22, 35, ...
六角數		Hn=n(2n1)		1, 6, 15, 28, 45, ...

可以證實 T₂₈₅ = P₁₆₅ = H₁₄₃ = 40755.

找出這之後的下一個既是五角數又是六角數的三角數。

public class Problem45
{
	public static void main(String[] args)
	{
		long start = System.currentTimeMillis();
		System.out.print("answer:  ");
		
		howmany();
		
		long end = System.currentTimeMillis();
		System.out.print("time:  ");
		System.out.println(end - start);
	}
	
	static void howmany()
	{
		for (int i = 144; ; i++)
		{
			long h = i * (2 * i - 1);
			
			double tp = (Math.sqrt(24 * h + 1) + 1) / 6;
			if ((int)tp != tp)
			{
				continue;
			}
			long tt =(int) Math.sqrt(h * 2);
			if (tt * (tt + 1) /2 != h)
			{
				continue;
			}
			System.out.println(h);
			break;
		}
	}
}

answer:  1533776805
time:  3