I’ve established that a_1=1 since a_3=5, but now I’m stuck.

In addition to the solution, I need to know how to prove this with induction.

This just reproduces the odd integers, so a_{128} = 2*128 - 1 → 255

Thanks Alan.

That is interesting. It looked so complicated.

Here's a derivation of the relation:

NB For the person who posted the question: Please note that this is not a proof by induction!

Thanks Alan :)