Triangle, pentagonal, and hexagonal numbers are generated by the following formulae:
Triangle T*n*=*n*(*n*+1)/2 1, 3, 6, 10, 15, ...
Pentagonal P*n*=*n*(3*n*−1)/2 1, 5, 12, 22, 35, ...
Hexagonal H*n*=*n*(2*n*−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.
三角形，五角形和六角形数字由以下公式生成：
三角形 T *n* = *n*（*n* +1）/ 2 1,3,6,10,15 ......
五角形 P *n* = *n*（3 *n* -1）/ 2 1,5,12,22,35 ......
六角形 H *n* = *n*（2 *n* -1） 1,6,15,28,45，......
可以证实T 285 = P 165 = H 143 = 40755。
找到下一个满足三角形 五角形 六角形的数字。
#include <stdio.h>
#include <inttypes.h>
int is_Pentagonal(int64_t x){
int64_t min = 1, max = x, mid;
while(min <= max){
mid = (min + max) / 2;
int64_t pen = mid * (3 * mid - 1) / 2;
if(pen == x) return 1;
if(pen < x) min = mid + 1;
else max = mid - 1;
}
return 0;
}
int main(){
int64_t n = 145;
while(!is_Pentagonal(n * (2 * n - 1))) n++;
printf("%"PRId64"\n", n * (2 * n - 1));
return 0;
}
