Unusual Speed Difference between Python and C++

Question

I recently wrote a short algorithm to calculate happy numbers in python. The program allows you to pick an upper bound and it will determine all the happy numbers below it.

Answer 1

With similar optimizations as PotatoSwatter I got time for 10000 numbers down from 1.063 seconds to 0.062 seconds (except I replaced itoa with standard sprintf in the original).

With all the memory optimizations (don't pass containers by value - in C++ you have to explicitly decide whether you want a copy or a reference; move operations that allocate memory out of inner loops; if you already have the number in a char buffer, what's the point of copying it to std::string etc) I got it down to 0.532.

The rest of the time came from using %10 to access digits, rather than converting numbers to string.

I suppose there might be another algorithmic level optimization (numbers that you have encountered while finding a happy number are themselves also happy numbers?) but I don't know how much that gains (there is not that many happy numbers in the first place) and this optimization is not in the Python version either.

By the way, by not using string conversion and a list to square digits, I got the Python version from 0.825 seconds down to 0.33 too.