MathDB

Bored of waiting for his plane to travel to the International Mathematics Olympiad, Daniel began to write powers of

2

in a list in his notebook as follows:

\bullet

Starting with the number

1

, Daniel writes the next power of

2

at the end of his list and reverses the order of the numbers in the list. Let us call such a modification of the list, including the first step, a move. The list in each of the first

4

moves it looks like this:

1 \,\,\,\, \to 2, 1 \,\,\,\, \,\,\,\, \to 4, 1, 2 \,\,\,\, \,\,\,\, \to 8, 2, 1, 4

Daniel plans to carry out operations until his plane arrives, but he is worried let the list grow too. After

2020

moves, what is the sum of the first

1010

numbers?

Problem Statement