2022 AMC 12B Problems/Problem 3
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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.
Note: In general, (where there are
"ones" on either side of the
) can be written as
, where the first term has
ones.
Solution 2
Let denote the digit
written
times and let
denote the concatenation of
,
, ...,
.
Observe that
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 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
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