$2^{2921}$ has $581$ digits and starts with a $4$. How many $2^n$'s starts with a $4$, where $0$ is the last digit?
Problem
Source: BdMO 2020 Final Primary Category Problem 12
Tags: number theory, number theory unsolved
Source: BdMO 2020 Final Primary Category Problem 12
Tags: number theory, number theory unsolved
$2^{2921}$ has $581$ digits and starts with a $4$. How many $2^n$'s starts with a $4$, where $0$ is the last digit?