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>
       
 
       
// ---------- code from my toolbox ----------

       
 
       
// greatest common divisor

       
template <typename T>
       
T gcd(T a, T b)
       
{
       
  while (a != 0)
       
  {
       
    T c = a;
       
    a = b % a;
       
    b = c;
       
  }
       
  return b;
       
}
       
 
       
// least common multiple

       
template <typename T>
       
T lcm(T a, T b)
       
{
       
  // parentheses avoid overflows for certain input values
       
  return a * (b / gcd(a, b));
       
}
       
 
       
// ---------- problem-specific code ----------

       
 
       
// count numbers up to limit with a given streak

       
unsigned long long bruteForce(unsigned long long limit, unsigned int streak)
       
{
       
  unsigned long long result = 0;
       
  for (unsigned long long i = 2; i < limit; i++)
       
  {
       
    unsigned int current = 1;
       
    while ((i + current - 1) % current == 0)
       
      current++;
       
 
       
    // counted one too far (the number after the streak ended)
       
    current--;
       
    // correct streak ?
       
    if (current == streak)
       
      result++;
       
  }
       
 
       
  return result;
       
}
       
 
       
// find result faster than the blink of an eye ...

       
unsigned long long solve(unsigned long long limit, unsigned int streak)
       
{
       
  // find least common multiple of 1..streak
       
  unsigned long long multiple = streak;
       
  for (unsigned long long i = 2; i < streak; i++)
       
    multiple = lcm(multiple, i);
       
 
       
  // each n - 1 which is a multiple of "multiple" is valid solution
       
  limit--;
       
  // the last number is excluded from the range, too
       
  limit--;
       
  auto atLeast = limit / multiple;
       
 
       
  // but there are a few number with a longer streaks !
       
  multiple = lcm(multiple, streak + 1ULL);
       
  auto tooMany = limit / multiple;
       
 
       
  // subtract them
       
  return atLeast - tooMany;
       
}
       
 
       
int main()
       
{
       
  //std::cout << bruteForce( 14, 3) << std::endl;
       
  //std::cout << bruteForce(100, 6) << std::endl;
       
 
       
  unsigned int limit = 31;
       
  std::cin >> limit;
       
 
       
  unsigned long long result = 0;
       
  unsigned long long pow4   = 4;
       
  for (unsigned int i = 1; i <= limit; i++)
       
  {
       
    //result += bruteForce(last, i);
       
    result += solve(pow4, i);
       
    pow4 *= 4;
       
  }
       
 
       
  // another problem solved !
       
  std::cout << result << std::endl;
       
  return 0;
       
}

This solution contains 15 empty lines, 18 comments and 1 preprocessor command.