Let $\Sigma:=\{ 0,1, \textrm{#} \}$ and the language $L=\{ bin(n)\textrm{#}w \in \Sigma ^* \mid n \in \mathbb N \, \land \, w \in \{ 0,1 \}^* \land |w| \leq n \}$
$\mid w \mid $ is the length of the word $w$. How can one describe a 2 tape TM that exactly accepts words from L.
I would really appreciate help to understand "how L looks like".
First I thought L is a string like "1101" and in decimal this would be 13. And so $\mid w\mid \leq13$, but now I wonder that $\mid w\mid \leq n$ would hold for any $n \in \mathbb N$. I am missing something but I do not know what..
P.S. There is a hint to use a TM that subtracts one from a given string.