dominant_primes.cpp

//The prime number sequence starts with: 2,3,5,7,11,13,17,19.... Notice that 2 is in position one.

//3 occupies position two, which is a prime-numbered position. Similarly, 5, 11 and 17 also occupy prime-numbered positions. We shall call primes such as 3,5,11,17 dominant primes because they occupy prime-numbered positions in the prime number sequence. Let's call this listA.

//As you can see from listA, for the prime range range(0,10), there are only two dominant primes (3 and 5) and the sum of these primes is: 3 + 5 = 8.

//Similarly, as shown in listA, in the range (6,20), the dominant primes in this range are 11 and 17, with a sum of 28.

//Given a range (a,b), what is the sum of dominant primes within that range? Note that a <= range <= b and b will not exceed 500000.

//Good luck!

bool IsPrime(int n) {
  for (int i = 2; i * i <= n + 1; ++i) {
    if (n % i == 0)
      return false;
  }
  
  return n > 1;
}

int solve(int a, int b){
  int sum = 0;
  
  for (int i = 3, j = 1; i <= b; ++i) {
    if (IsPrime(i)) {
      ++j;
      if (i >= a && IsPrime(j))
        sum += i;
    }
  }
  
  return sum;
}