My code

… was written in C++11 and can be compiled with G++, Clang++, Visual C++. You can download it, too. Or just jump to my GitHub repository.

       
#include <iostream>
       
#include <string>
       
#include <algorithm>
       
 
       
// base: decimal=10, binary=2

       
std::string num2str(unsigned int x, unsigned int base)
       
{
       
  std::string result;
       
  while (x > 0)
       
  {
       
    auto digit = x % base;
       
    x         /= base;
       
    result.insert(0, 1, char(digit + '0'));
       
  }
       
  return result;
       
}
       
 
       
// true if string is a palindrome

       
bool isPalindrome(const std::string& s)
       
{
       
  auto other = s;
       
  std::reverse(other.begin(), other.end());
       
  return other == s;
       
}
       
 
       
// I was quite surprised that the basic brute-force approach is sufficiently fast ...

       
int main()
       
{
       
  unsigned int limit, base; // limit = 1000000 and base = 2
       
  std::cin >> limit >> base;
       
 
       
  unsigned int sum = 0;
       
  for (unsigned int x = 1; x < limit; x++)
       
    if (isPalindrome(num2str(x, 10)) &&  // palindrome in base 10 ?
       
        isPalindrome(num2str(x, base)))  // palindrome in base k ?
       
      // yes, double palindrome
       
      sum += x;
       
 
       
  std::cout << sum << std::endl;
       
  return 0;
       
}

This solution contains 5 empty lines, 4 comments and 3 preprocessor commands.