| ||The fibonacci sequence is a sequence of integers in which each number is equal to the sum of the two preceding numbers. The first two integers in the sequence are both 1. Formally:
The beginning of this sequence is 1,1,2,3,5,8,13,21.
- F1 = 1
- F2 = 1
- Fi = Fi-1 + Fi-2 for each i > 2
We'll define the fibonacci position of an integer greater than or equal to 1 as follows:
As examples, if FP(n) is the fibonacci position of n,
- The fibonacci position of 1 is 2 (since F2 = 1)
- The fibonacci position of any integer n > 1 such that Fi = n is i
- The fibonacci position of any integer n > 1 such that it is strictly between Fi and Fi+1 is i+(n-Fi)/(Fi+1-Fi) (informally, this means it is linearly distributed between Fi and Fi+1)
FP(1)=2 (first rule)
FP(5)=5 (second rule F5 = 5)
FP(4)=4.5 (third rule, is right in the middle of F4 = 3 and F5 = 5)
Given an integer n, return its fibonacci position as a double.