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esthetic n.  and  odious n.

First numbers that belong to both sets:

21, 32, 56, 67, 76, 87, 98, 121, 234, 321, 345, 434, 454, 545, 565, 654, 656, 678, 767, 787, 789, 878, 1010, 1012, 1234, 2101, 2123, 2323, 2345, 3210, 3212, 3234, 3434, 3454, 4321, 4345, 4543, 4545, 4565, 5434, 5454, 5456, 5656, 5678, 6565, 6767, 7654, 7678, 7876, 7898, 8765, 8987, 8989, 9878, 9898, 10101, 10121, 12121, 12323, 12343, 21010, 21012, 21232, 23234, 23432, 23456, 32121, 32323, 32343, 34321, 34343, 34567, 43210, 43212, 43234, 43432, 45434, 45656, 45678, 54321, 54345, 54543, 54545, 54567, 56545, 56565, 56767, 56787, 56789, 65432, 65454, 65456, 65656, 65678, 67654, 67678, 67876, 67898, 76567, 76765, 76787, 76789, 78767, 78787, 78789, 87654, 87678, 87878, 89876, 98767, 101010, 101012, 101210, 101212, 101234, 121010, 121012, 121210, 121212, 121234, 123232, 123432, 210121, 212101, 212123, 212323, 212343, 232101, 232123, 232323, 232343, 234321, 234343, 234567, 321010, 321012, 321210, 321212, 321232, 323232, 323432, 323456, 343234, 343432, 343456, 345434, 345654, 345678, 432121, 432323, 432343, 434321, 434343, 434543, 434545, 434567, 454323, 454343, 454565, 456543, 456567, 456767, 456787, 456789, 543210, 543212, 543234, 543432, 543456, 545432, 545454, 545456, 545656, 545678, 565432, 565656, 565678, 567654, 567678, 567876, 567898, 654323, 654343, 654565, 656543, 656567, 656767, 676567, 676765, 676787, 676789, 678767, 765432, 765454, 765456, 765654, 765676, 767656, 767676, 767876, 767898, 787654, 787678, 787876, 787898, 789876, 876543, 876567, 876765, 876787, 876789, 878765, 878987, 878989, 898765, 898787, 898789, 987656, 987676, 987878, 989876, 989898, 1010101, 1010123, 1012101, 1012123, 1012321, 1012345, 1210101, 1210123, 1212121, 1212323, 1212343, 1232101, 1232123, 1232323, 1232343, 1234323, 1234345, 1234543, 1234545, 1234567, 2101010, 2101012, 2101232, 2121010, 2121012, 2121232, 2123210, 2123212, 2123234, 2123434, 2123454, 2123456, 2321010, 2321012, 2321234, 2323232, 2323434, 2323454, 2323456, 2343210, 2343212, 2343232, 2343432, 2343456, 2345432, 2345454, 2345456, 2345656, 2345676, 3210123, 3212121, 3212323, 3212343, 3232121, 3232323, 3232343, 3234321, 3234343.

Some larger examples :