So I was watching this numberphile video and it explained how the iteration under the function $f(x) = 2x + 1$, starting with $x_1=1$, (the mersenne sequence) always produced a number with one or more prime divisors not seen before. EXCEPT 63. Dr Krigger, the mathematician who was explaining this, said that this had to do with the fact that 63 was the 6th element of the sequence.
I tried to find an explanation for this but wasn't very successful. A simple explanation to this, if there's any, would be great but complicated ones are fine too.
