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nude n.  and  plaindrome

First numbers that belong to both sets:

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 15, 22, 24, 33, 36, 44, 48, 55, 66, 77, 88, 99, 111, 112, 115, 122, 124, 126, 128, 135, 144, 155, 168, 222, 224, 244, 248, 288, 333, 336, 366, 444, 448, 488, 555, 666, 777, 888, 999, 1111, 1112, 1113, 1115, 1116, 1122, 1124, 1128, 1144, 1155, 1222, 1224, 1236, 1244, 1248, 1266, 1288, 1335, 1344, 1368, 1444, 1448, 1488, 1555, 1888, 2222, 2224, 2226, 2244, 2248, 2288, 2444, 2448, 2488, 2688, 2888, 3333, 3336, 3339, 3366, 3444, 3555, 3666, 3888, 4444, 4448, 4488, 4888, 5555, 6666, 6888, 7777, 8888, 9999, 11111, 11112, 11115, 11122, 11124, 11128, 11133, 11136, 11144, 11155, 11166, 11222, 11224, 11226, 11244, 11248, 11288, 11355, 11444, 11448, 11488, 11555, 11688, 11888, 12222, 12224, 12244, 12248, 12288, 12336, 12366, 12444, 12448, 12488, 12666, 12888, 13335, 13344, 13368, 13377, 13488, 14444, 14448, 14488, 14688, 14888, 15555, 18888, 22222, 22224, 22236, 22244, 22248, 22266, 22288, 22344, 22368, 22444, 22448, 22488, 22888, 23448, 23688, 24444, 24448, 24488, 24888, 26688, 27888, 28888, 33333, 33336, 33366, 33399, 33444, 33555, 33666, 33888, 34488, 36666, 36888, 44444, 44448, 44488, 44688, 44888, 48888, 55555, 66666, 66888, 77777, 88888, 99999, 111111, 111112, 111115, 111122, 111124, 111126, 111128, 111135, 111144, 111155, 111168, 111222, 111224, 111244, 111248, 111288, 111333, 111336, 111339, 111366, 111444, 111448, 111488, 111555, 111666, 111888, 112222, 112224, 112236, 112244, 112248, 112266, 112288, 112344, 112368, 112444, 112448, 112488, 112888, 113337, 113355, 113448, 113688, 114444, 114448, 114488, 114888, 115555, 116688, 117999, 118888, 122222, 122224, 122226, 122244, 122248, 122288, 122444, 122448, 122488, 122688, 122888, 123336, 123366, 123444, 123666, 123888, 124444, 124448, 124488, 124888, 126666, 126888, 128888, 133335, 133344, 133368, 133488, 134448, 134688, 135555, 138888, 144444.

Some larger examples :