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esthetic n.  and  pernicious n.

First numbers that belong to both sets:

10, 12, 21, 34, 56, 65, 67, 76, 87, 98, 121, 234, 321, 345, 434, 454, 545, 565, 654, 656, 678, 787, 789, 878, 1010, 1012, 1234, 2101, 2123, 2323, 2345, 3210, 3212, 3234, 3434, 4321, 4345, 4545, 4565, 5434, 5454, 5456, 5656, 5678, 6565, 7678, 7876, 8765, 8987, 8989, 9878, 9898, 10121, 12323, 12343, 21010, 21012, 21232, 23234, 23432, 23456, 32121, 32343, 34321, 34343, 34567, 43210, 43212, 43234, 43432, 45656, 54321, 54345, 54545, 56565, 56767, 56787, 56789, 65432, 65454, 65456, 65656, 65678, 67654, 67678, 67876, 67898, 76765, 76787, 76789, 78767, 87678, 101010, 101012, 121210, 121212, 123232, 123432, 212123, 212323, 212343, 232123, 232343, 234343, 321010, 321012, 321210, 321212, 323432, 432121, 432343, 434321, 434543, 454323, 454343, 454565, 456767, 456787, 456789, 543234, 543432, 543456, 545432, 545456, 565432, 565656, 567678, 567876, 654343, 654565, 656767, 676567, 676765, 676787, 676789, 678767, 765432, 765454, 765654, 765676, 767656, 767676, 767876, 767898, 787654, 787876, 876543, 876765, 876787, 876789, 878765, 878987, 878989, 898765, 898787, 898789, 987656, 987878, 989876, 989898, 1010101, 1010123, 1012101, 1012123, 1012321, 1012345, 1210101, 1210123, 1212121, 1212323, 1232101, 1232123, 1232323, 1232343, 1234323, 1234345, 1234543, 1234545, 1234567, 2101010, 2101012, 2121232, 2123454, 2123456, 2321010, 2321012, 2321234, 2323434, 2323456, 2343232, 2343432, 2343456, 2345432, 2345454, 2345456, 2345656, 2345676, 3210123, 3212323, 3232121, 3232343, 3234343, 3234567, 3432121, 3432321, 3432345, 3434321, 3434343, 3434543, 3454323, 3454345, 3454543, 3454545, 3454567, 3456545, 3456565, 3456767, 3456787, 3456789, 4321010, 4321012, 4321234, 4323232, 4323434, 4323454, 4343232, 4343432, 4343456, 4345454, 4345654, 4345678, 4543210, 4543212, 4543232, 4543434, 4543454, 4545432, 4545454, 4545456, 4545656, 4545678, 4565432, 4565654, 4565676, 4567654, 4567678, 4567878, 5432101, 5432123, 5432343, 5434321, 5434567, 5454321, 5454343, 5454565, 5456565, 5456765, 5456787, 5456789, 5654321, 5654345, 5656545, 5656767, 5656787, 5656789, 5676543, 5676567, 5678765, 5678987, 5678989, 6543232, 6543434, 6543454, 6545454, 6545654, 6545678, 6565434, 6565454, 6565654, 6565676.

Some larger examples :