Is there a manipulation that can be performed on the natural number sequence (1,2,3,...) in order to give the Fibonacci sequence?
I know the recurrence relation starting from 1,1 and successively adding the two previous numbers of the sequence. However, while this gives the Fibonacci sequence, it is not a manipulation of the natural number sequence as a whole. My question is whether there is a certain operation that can be repeatedly applied to the natural numbers as a whole (ie the sequence of natural numbers) to give the Fibonacci numbers.