Your topic reminds me of the old days in high school. Smerits are generated like radioactive decay and above sum is a geometric progression
I still remember that there's a general method to calculate this sum:

Assume that S =           16384 + 8192   + 4096 + 2048 +1024 + 512 + 256 + 128 + 64 +32 + 16 + 8 + 4 + 2 + 1
                      =           2¹⁴ + 2¹³ + 2¹² + ... + 2¹ +2⁰ (*)
then          2S  = 2¹⁵ + 2¹⁴ + 2¹³ + ... +2² +2¹           (**)

(**) - (*) side by side, then S = 2¹⁵-1 =  32767

Btw, it's an interesting discovery OP.