MathDB

Let

k

be a positive integer. Scrooge McDuck owns

k

gold coins. He also owns infinitely many boxes

B_1, B_2, B_3, \ldots

Initially, bow

B_1

contains one coin, and the

k-1

other coins are on McDuck's table, outside of every box. Then, Scrooge McDuck allows himself to do the following kind of operations, as many times as he likes: - if two consecutive boxes

B_i

and

B_{i+1}

both contain a coin, McDuck can remove the coin contained in box

B_{i+1}

and put it on his table; - if a box

B_i

contains a coin, the box

B_{i+1}

is empty, and McDuck still has at least one coin on his table, he can take such a coin and put it in box

B_{i+1}

. As a function of

k

, which are the integers

n

for which Scrooge McDuck can put a coin in box

B_n

Problem Statement