Question 142
Does there exist a function $f: \mathbb{N} \to \mathbb{N}$ such that
$$
f(f(n+1)) = f(f(n)) + 2^{n-1}
$$
for any positive integer $n$? (As usual, $\mathbb{N}$ stands for the set of all positive integers.)
$$
f(f(n+1)) = f(f(n)) + 2^{n-1}
$$
for any positive integer $n$? (As usual, $\mathbb{N}$ stands for the set of all positive integers.)