[math-fun] Digits 4 digits: last term?

Hello Math-Fun, Let's call S the lexicographically earliest sequence of distinct integers > 0 with the following property: «The a(n)th digit of S is the number of digits used by a(n)». [for example, if the 85th digit of S is a 4, then a(85) uses exactly 4 digits] Questions: 1) how many terms has S? 2) what is the last term of S? There are enough elements above to ask, but if you want to see how S starts, and have some more explanations, please click here (link to my personal blog): https://bit.ly/2Ss2BFE Best, É.