I created this puzzle. Find the next number in the sequence and the logic behind it.$$2, 1536, 5, 1792, 23, 1184, 53, 1168, 113, 1048, 137, 1384, 179, 1576, 311, 1268, 431, 1234, 719, 2026, 1031, 1097, 1499$$
Look closely at each number and its properties. This will help.
Hint 1:
Hint 2: