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1

Part of 2000 Argentina National Olympiad

Problems(1)

sequence of digits by naturals

Source: Argentina 2000 OMA L3 p1

5/12/2024
The natural numbers are written in succession, forming a sequence of digits12345678910111213141516171819202122232425262728293031…12345678910111213141516171819202122232425262728293031\ldotsDetermine how many digits the natural number has that contributes to this sequence with the digit in position 10200010^{2000}. Clarification: The natural number that contributes to the sequence with the digit in position 1010 has 22 digits, because it is 1010; The natural number that contributes to the sequence with the digit at position 10210^2 has 22 digits, because it is 5555.
number theoryDigits