All Questions

Let $f(n)$ be A053645, distance to largest power of $2$ less than or equal to $n$; write $n$ in binary, change the first digit to zero, and convert back to decimal. Let $g(n)$ be A007814, the ...

Let $f(n)$ be A007814, the exponent of the highest power of $2$ dividing $n$, a.k.a. the binary carry sequence, the ruler sequence, or the $2$-adic valuation of $n$. Then we have an integer sequence ...

Let $p$ and $q$ be integers. Let $f(n)$ be A007814, the exponent of the highest power of $2$ dividing $n$, a.k.a. the binary carry sequence, the ruler sequence, or the $2$-adic valuation of $n$. Then ...

Let $m\geq 2$ be a fixed integer. Let $$f(n):=\begin{cases} mf\left(\frac{n}{m}\right),&\text{if $n\mod m = 0$;}\\ 1,&\text{otherwise} \end{cases}$$ then if we have $$a(n):=\begin{cases} 1,&...

Let $p$ and $q$ be integers. Let $f(n)$ be A007814, the exponent of the highest power of $2$ dividing $n$, a.k.a. the binary carry sequence, the ruler sequence, or the $2$-adic valuation of $n$. Then ...