It’s the path that maximises time, not distance. Technically the path that maximises time could look the same as the path that minimises distance, they could just sit down and wait decades until a minute before they die of natural causes and then get up and head to the end, and that’s assuming that they need to arrive alive.

I think you have to include 2^0 for that to be true?

e.g 2^0 = 1, 2^1 = 2 2^0 + 2^1 = 1 + 2 = 3, 2^2 = 4 … 7, 8 15,16 31, 32 etc.

Only 32