2014 AMC 10A Problems/Problem 24
A sequence of natural numbers is constructed by listing the first , then skipping one, listing the next , skipping , listing , skipping , and, on the th iteration, listing and skipping . The sequence begins . What is the th number in the sequence?
If we list the rows by iterations, then we get
so that the th number is the th number on the th row. () The last number of the th row (with 999 terms) is , (we add the because of the numbers we skip) so our answer is
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