2022 AMC 12B Problems/Problem 3
Contents
Problem
How many of the first ten numbers of the sequence , , , ... are prime numbers?
Solution 1
Write , , . It becomes clear that of these numbers are prime.
In general, (where there are 's on either side of the ) can be written as , where the first term has 's.
Solution 2
Let denote the digit written times and let denote the concatenation of , , ..., .
Observe that
Since for all positive integers and , is equal to
Both terms are integers larger than since , so of the numbers of the sequence are prime.
See Also
2022 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 2 |
Followed by Problem 4 |
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