No loop; No recursion; 我没找到规律 但是从讨论区看到别人的思路：
If N is a power of 3:
3^X == Nlog (3^X) == log NX log 3 == log NX == (log N) / (log 3)X must be an integer.代码：
public class Solution {
public boolean isPowerOfThree(int n) {
double diff = 10e-15;
double x = Math.log(n)/Math.log(3);
return Math.abs( x - Math.round(x)) <= diff;
}
}
Jan 14 - Power of three; Math; Integer; Digit;
原文：http://www.cnblogs.com/5683yue/p/5132198.html