problem045.cpp

#include <cmath>
#include <iostream>

bool isPentagonal(long long n)
{
 return fmod(sqrt(24 * n + 1), 6) == 5;
}

int nextTriPentaHexagonal(int n)
{
 int hexIndex = (sqrt(8 * n + 1) + 1) / 4;
 int hex = hexIndex * (2 * hexIndex - 1);
 int inc = 4 * hexIndex + 1;
 for (;;) {
 hex += inc;
 if (isPentagonal(hex)) {
 return hex;
 }
 inc += 4;
 }
}

int main()
{
 std::cout << "Answer: " << nextTriPentaHexagonal(40755) << '\n';
 return 0;
}