Is there a standard notation for 'written in base a'? I am considering a procedure in which it is useful to switch between bases and operate on a number in these different bases (take decimal truncations etc). What matters here is the actual sequnce of digits. Now at the end of an operation, I have a sequnce of digits corresponding to a number in base 3 say, and I wish now to express the sequence which is "the number corresponding to the sequnce written in base 3, now written in base 10". Is there a nice notation for this that I am not aware of?

It's common to write
$$
13 = 111_3 .
$$
With no subscript, the convention is that you have written the base $10$ expansion of the number.
You can safely use that notation, Just explain it to your reader the first time.
The base (the subscript) is written in base 10, so
$$
A_{16} = 10
$$
and
$$
10_n = n .
$$
