[2015-10-14] Challenge #236 [Intermediate] Fibonacci-ish Sequence : dailyprogrammer

[2015-10-14] Challenge #236 [Intermediate] Fibonacci-ish Sequence : dailyprogrammer

The Fibonacci Sequence is a famous integer series in the field of mathematics. The sequence is recursively defined for n > 1 by the formula f(n) = f(n-1) + f(n-2). In plain english, each term in the sequence is found by adding the previous two terms together. Given the starting values of f(0) = 0 and f(1) = 1 the first ten terms of the sequence are:

0 1 1 2 3 5 8 13 21 34

We will notice however that some numbers are left out of the sequence and don't get any of the fame, 9 is an example. However, if we were to start the sequence with a different value for f(1) we will generate a new sequence of numbers. Here is the series for f(1) = 3:

0 3 3 6 9 15 24 39 102 165

We now have a sequence that contains the number 9. What joy!
Today you will write a program that will find the lowest positive integer for f(1) that will generate a Fibonacci-ish sequence containing the desired integer (let's call it x).

Input description

Your input will be a single positive integer x.

Sample Input 1: 21

Sample Input 2: 84

Output description

The sequence of integers generated using the recursion relation starting from 0 and ending at the desired integer x with the lowest value of f(1).

Sample Output 1: 0 1 1 2 3 5 8 13 21

Sample Output 2: 0 4 4 8 12 20 32 52 84

Read full article from [2015-10-14] Challenge #236 [Intermediate] Fibonacci-ish Sequence : dailyprogrammer