František Nudílek was engaged in writing consecutive natural numbers. He started like this: 1234567891011... After a while, he got bored, finished writing the current number, and critically examined his creation. He noticed that in the sequence of digits he had written, there were five consecutive ones.

1. How many consecutive natural numbers did František have to write at a minimum?
2. How many digits did František have to write at a minimum?
1. To have five ones in a row, numbers greater than 110 must be written, and the sequence looks like this:

$$
123456789101112 \ldots 110 \underline{111112} \ldots
$$

František wrote at least 112 consecutive natural numbers.

2. For counting the digits, we realize that in the written sequence, there are 9 one-digit numbers (numbers 1-9), 90 two-digit numbers (numbers 10-99), and at least 13 three-digit numbers (numbers 100-112). In total, František wrote at least $9 + 90 \cdot 2 + 13 \cdot 3 = 228$ digits.