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plaindrome  and  tau n.

First numbers that belong to both sets:

1, 2, 8, 9, 12, 18, 24, 36, 56, 88, 128, 136, 156, 225, 228, 248, 288, 344, 348, 444, 448, 468, 488, 568, 1112, 1116, 1224, 1236, 1248, 1256, 1336, 1344, 1356, 1368, 1448, 1668, 1688, 1788, 2248, 2344, 2388, 2456, 2488, 2556, 2688, 3368, 3448, 3456, 3688, 4456, 4568, 4668, 4788, 5556, 5688, 11136, 11148, 11244, 11268, 12228, 12248, 12344, 12348, 12456, 12468, 12568, 12588, 12888, 13336, 13344, 13356, 13788, 13888, 14488, 14556, 14688, 14888, 15588, 16668, 16788, 16888, 22356, 22368, 22668, 22888, 23336, 23388, 24444, 24448, 24468, 24488, 24588, 25668, 26888, 33336, 33444, 33468, 33489, 33688, 33888, 34488, 34688, 35556, 38888, 44448, 44456, 44568, 45688, 46668, 46888, 55668, 55688, 55788, 57888, 66688, 66888, 67788, 111224, 111256, 111368, 111448, 111488, 112224, 112248, 112256, 112338, 112356, 112448, 112456, 112568, 112788, 113344, 113556, 113688, 114468, 114568, 115688, 115788, 117888, 122456, 122888, 123444, 123468, 123588, 123688, 124668, 124788, 125556, 125568, 125888, 128888, 133344, 133356, 133668, 133788, 134488, 134556, 134688, 135588, 136788, 144444, 144468, 144488, 144588, 145688, 145788, 155556, 156888, 158888, 166788, 177888, 222228, 222336, 222344, 222444, 222468, 222588, 223336, 223688, 224448, 224456, 224556, 224568, 224888, 225688, 225888, 226688, 226788, 228888, 233336, 233344, 233556, 233568, 234488, 236888, 237888, 244456, 244668, 244788, 245556, 245888, 247788, 256788, 277888, 333348, 333448, 333468, 333588, 336888, 337788, 344448, 344556, 345888, 347778, 355788, 367788, 388888, 444456, 444468, 444588, 445668, 445688, 446688, 455556, 455688, 457788, 556788, 566688, 588888, 688888, 777888, 1111112, 1111116, 1111144, 1111168, 1111336, 1111356, 1111488, 1111668, 1111788, 1112388, 1112448, 1113336, 1113348, 1113444, 1113468, 1113888, 1114788, 1114888, 1118888, 1122248, 1122348, 1122568, 1122588, 1123336, 1123456, 1123488, 1124448, 1124456, 1124568, 1124888, 1126668, 1128888, 1133336, 1133368, 1133388, 1133556, 1133888, 1134468, 1134488, 1135688, 1135788, 1136888, 1144448, 1144888, 1145568, 1147788, 1155688, 1156888, 1166688.

Some larger examples :