A135479 Sorted list of primitive strings that can be obtained by starting with 123 and repeatedly doubling any substring in place.

123, 12123, 12323, 123123, 1212123, 1212323, 1232323, 12123123, 12312123, 12312323, 12313123, 12323123, 121212123, 121212323, 121232123, 121232323, 123123123, 123212323, 123232323, 1212123123, 1212312123, 1212312323, 1212313123, 1212323123, 1231212123