Given $n$, exist $k$ such that $2^k$ contains $n$ as string.

Asked Sep 26 '19 at 22:10

Active Sep 26 '19 at 22:10

Viewed 76 times

I have this doubt:

Given $n\in \mathbb{N}$, does exist $k\in \mathbb{N}$ such that $2^k$ contains $n$ as a string in it?

For example, $53$ is in $2^{16}=65\color{red}{53}6$.

I just thought the problem right now so I don't have knowledge if it's even possible to solve it, but sounds a very nice problem. Does someone has an idea?

asked Sep 26 '19 at 22:10

iam_agf

5,438

See also this and this. – Arthur Sep 26 '19 at 22:22
https://oeis.org/A030000 is worth a look. – Barry Cipra Sep 26 '19 at 22:26
@Arthur: that question asked for the string to start $2^n$, while here we are permitted to have it in the middle. Still, that one solves the problem. – Ross Millikan Sep 26 '19 at 22:42

Given $n$, exist $k$ such that $2^k$ contains $n$ as string.

0 Answers0