3 problems

Let $f'(n)$ be the companion sequence described above, and let $g'(m)$ denote the position where $f'(n)$ first takes the value $m$. Let $g(m)$ denote the corresponding position for…

For an odd positive integer $k$, define the set of $k$-flimsy numbers by … where $s_2(n)$ denotes the number of $1$'s in the binary expansion of $n$. Stolarsky's density conjecture…

Let $j$ be the number of $0$'s in the binary representation of a number, and let $s$ be a binary string with length $|s|=j$ that begins with $1$ and ends with $0$. Write…