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 } \{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.


The answer is 5.

Mateo Matijasevick by Mateo Matijasevick , 22, Colombia

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1 solution

J D
Jun 2, 2016

1, 3, -2, 34, 2014

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Prove that this is the shortest eccentric list. Find all the lists that consist of 5 terms.

Mateo Matijasevick - 5 years ago

Yes is there any proof for this ...................if yes please try to give it

Abhisek Mohanty - 4 years, 11 months ago

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