MathDB

Given a set

A=\{1;2;...;4044\}

. They color

2022

numbers of them by white and the rest of them by black. With each

i\in A

, called the important number of

i

be the number of all white numbers smaller than

i

and black numbers larger than

i

. With every natural number

m

, find all positive integers

k

that exist a way to color the numbers that can get

k

important numbers equal to

m

6