2022 AMC 12B Problems/Problem 3
Problem
How many of the first ten numbers of the sequence ,
,
, ... are prime numbers?
Solution 1
Let denote the digit
written
times and let
denote the concatenation of
,
, ...,
.
Observe that
Clearly, both terms are larger than
since
, hence all the numbers of the sequence are
, and we're done!