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amenable n.  and  esthetic n.

First numbers that belong to both sets:

12, 21, 32, 45, 56, 65, 76, 89, 101, 121, 212, 232, 321, 345, 432, 456, 545, 565, 656, 676, 765, 789, 876, 989, 1012, 1212, 1232, 2101, 2121, 2321, 2345, 3212, 3232, 3432, 3456, 4321, 4345, 4545, 4565, 5432, 5456, 5656, 5676, 6545, 6565, 6765, 6789, 7656, 7676, 7876, 8765, 8789, 8989, 9876, 10101, 10121, 12101, 12121, 12321, 12345, 21012, 21212, 21232, 23212, 23232, 23432, 23456, 32101, 32121, 32321, 32345, 34321, 34345, 34545, 34565, 43212, 43232, 43432, 43456, 45432, 45456, 45656, 45676, 54321, 54345, 54545, 54565, 56545, 56565, 56765, 56789, 65432, 65456, 65656, 65676, 67656, 67676, 67876, 76545, 76565, 76765, 76789, 78765, 78789, 78989, 87656, 87676, 87876, 89876, 98765, 98789, 98989, 101012, 101212, 101232, 121012, 121212, 121232, 123212, 123232, 123432, 123456, 210101, 210121, 212101, 212121, 212321, 212345, 232101, 232121, 232321, 232345, 234321, 234345, 234545, 234565, 321012, 321212, 321232, 323212, 323232, 323432, 323456, 343212, 343232, 343432, 343456, 345432, 345456, 345656, 345676, 432101, 432121, 432321, 432345, 434321, 434345, 434545, 434565, 454321, 454345, 454545, 454565, 456545, 456565, 456765, 456789, 543212, 543232, 543432, 543456, 545432, 545456, 545656, 545676, 565432, 565456, 565656, 565676, 567656, 567676, 567876, 654321, 654345, 654545, 654565, 656545, 656565, 656765, 656789, 676545, 676565, 676765, 676789, 678765, 678789, 678989, 765432, 765456, 765656, 765676, 767656, 767676, 767876, 787656, 787676, 787876, 789876, 876545, 876565, 876765, 876789, 878765, 878789, 878989, 898765, 898789, 898989, 987656, 987676, 987876, 989876, 1010101, 1010121, 1012101, 1012121, 1012321, 1012345, 1210101, 1210121, 1212101, 1212121, 1212321, 1212345, 1232101, 1232121, 1232321, 1232345, 1234321, 1234345, 1234545, 1234565, 2101012, 2101212, 2101232, 2121012, 2121212, 2121232, 2123212, 2123232, 2123432, 2123456, 2321012, 2321212, 2321232, 2323212, 2323232, 2323432, 2323456, 2343212, 2343232, 2343432, 2343456, 2345432, 2345456, 2345656, 2345676, 3210101, 3210121, 3212101, 3212121, 3212321, 3212345, 3232101, 3232121, 3232321, 3232345, 3234321, 3234345, 3234545.

Some larger examples :