Nicholas J. J. Smith is trying to show in section 2.5.6 on Finite Alphabets that one does not need to use infinitely many symbols: "five connectives, two parentheses, and infinitely many basic propositions." (page 48)
Instead one can replace the infinitely many symbols for basic propositions by recursive definitions. He replaces the definition of basic proposition as an infinite set of symbols with a recursive definition using only the letters of the alphabet and the digits from 0 to 9. This recursive definition uses the idea of a "finite string of digits" or "fsd" which he also recursively defines.
Consider the question, And why don't propositions have subscripts 0 and 1?
Basic propositions can have the symbols 0 and 1 along with the other digits. The only restriction is that 0 may not be used in the first position of an fsd. Smith is trying to avoid subscripts that start with 0.
Note the base clause:
Each of the single digits 1,..., 9 is an fsd.
This means that the first digit can be any one of 1, 2, 3, 4, 5, 6, 7, 8, or 9. However, it cannot be 0. Any following digit, however, may include 0 based on the recursive clause:
If x is an fsd and y is one of the digits 0,..., 9 then xy is an fsd.
Smith, N. J. (2012). Logic: The laws of truth. Princeton University Press.