MathDB
sequence of digits by naturals

Source: Argentina 2000 OMA L3 p1

May 12, 2024
number theoryDigits

Problem Statement

The natural numbers are written in succession, forming a sequence of digits1234567891011121314151617181920212223242526272829303112345678910111213141516171819202122232425262728293031\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.