The positive integers are written consecutively in rows, with seven integers in each row. That is, the first row contains the integers \(1\), \(2\), \(3\), \(4\), \(5\), \(6\), and \(7\). The second row contains the integers \(8\), \(9\), \(10\), \(11\), \(12\), \(13\), and \(14\). The third row contains the integers \(15\), \(16\), \(17\), \(18\), \(19\), \(20\), and \(21\), and so on.
The row sum of a row is the sum of the integers in the row. For example, the row sum of the first row is \(1+2+3+4+5+6+7=28\).
Determine the numbers in the row that has a row sum closest to \(2024\).
