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esthetic n.  and  evil n.

First numbers that belong to both sets:

10, 12, 23, 34, 43, 45, 54, 65, 78, 89, 101, 123, 210, 212, 232, 323, 343, 432, 456, 543, 567, 676, 765, 876, 898, 987, 989, 1210, 1212, 1232, 2121, 2321, 2343, 3232, 3432, 3456, 4323, 4343, 4567, 5432, 5654, 5676, 6543, 6545, 6567, 6765, 6787, 6789, 7656, 7676, 7878, 8767, 8787, 8789, 9876, 10123, 12101, 12123, 12321, 12345, 21210, 21212, 21234, 23210, 23212, 23232, 23434, 23454, 32101, 32123, 32321, 32345, 34323, 34345, 34543, 34545, 34565, 43232, 43434, 43454, 43456, 45432, 45454, 45456, 45654, 45676, 54323, 54343, 54565, 56543, 56567, 56765, 65434, 65654, 65676, 67656, 67676, 67878, 76543, 76545, 76565, 76767, 78765, 78987, 78989, 87656, 87676, 87876, 87898, 89878, 89898, 98765, 98787, 98789, 98987, 98989, 101232, 121232, 123210, 123212, 123234, 123434, 123454, 123456, 210101, 210123, 212121, 212321, 212345, 232121, 232321, 232345, 234323, 234345, 234543, 234545, 234565, 321234, 323210, 323212, 323234, 323434, 323454, 343210, 343212, 343232, 343434, 343454, 345432, 345454, 345456, 345656, 345676, 432101, 432123, 432321, 432345, 434323, 434345, 434565, 454321, 454345, 454543, 454545, 454567, 456545, 456565, 456765, 543232, 543434, 543454, 545434, 545654, 545676, 565434, 565454, 565456, 565654, 565676, 567656, 567676, 567878, 654321, 654345, 654543, 654545, 654567, 656545, 656565, 656765, 656787, 656789, 676543, 676545, 676565, 676767, 678765, 678787, 678789, 678987, 678989, 765434, 765656, 765678, 767654, 767678, 767878, 787656, 787676, 787878, 789878, 789898, 876545, 876565, 876767, 878767, 878787, 878789, 898767, 898987, 898989, 987654, 987678, 987876, 987898, 989878, 1010121, 1012121, 1012323, 1012343, 1210121, 1212101, 1212123, 1212321, 1212345, 1232121, 1232321, 1232345, 1234321, 1234343, 1234565, 2101210, 2101212, 2101234, 2121210, 2121212, 2121234, 2123232, 2123432, 2321210, 2321212, 2321232, 2323210, 2323212, 2323234, 2323432, 2343234, 2343434, 2343454, 2345434, 2345654, 2345678, 3210101, 3210121, 3212101, 3212123, 3212321, 3212345, 3232101, 3232123, 3232321, 3232345, 3234323, 3234345, 3234543, 3234545, 3234565, 3432101, 3432123, 3432323.

Some larger examples :