# Eccentric Lists

**Number Theory**Level 4

A list of integers is called *eccentric* if it starts with 1, and the sum of every two consecutive elements of the list is a power of 2. For example,

\[ \{1,3,29,-13,15 \} \]

is an eccentric list. Find the number of terms of the shortest eccentric list in which the integer 2014 appears in the list.

**Bonus**:

Find all the eccentric lists of this length that contain the number 2014.

Try out with another powers or another numbers and show us your results.