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arithmetic n.  and  esthetic n.

First numbers that belong to both sets:

21, 23, 43, 45, 54, 56, 65, 67, 78, 87, 89, 101, 123, 210, 212, 321, 323, 343, 345, 432, 434, 454, 456, 543, 545, 565, 654, 678, 765, 767, 787, 789, 878, 987, 989, 1012, 1212, 2101, 2121, 2123, 2321, 2323, 2343, 2345, 3210, 3212, 3234, 3432, 3454, 4321, 4323, 4343, 4345, 4543, 4545, 4565, 4567, 5432, 5434, 5454, 5654, 5656, 5676, 5678, 6545, 6565, 6567, 6765, 6767, 6787, 6789, 7654, 7656, 7676, 7678, 7876, 7878, 7898, 8765, 8767, 8787, 8789, 8987, 8989, 9878, 10101, 10121, 10123, 12101, 12121, 12123, 12323, 12343, 12345, 21010, 21012, 21210, 21212, 21234, 23210, 23454, 32101, 32121, 32123, 32321, 32323, 32343, 32345, 34321, 34323, 34343, 34345, 34543, 34545, 34565, 34567, 43232, 43434, 43454, 43456, 45432, 45454, 45654, 45656, 45678, 54321, 54323, 54343, 54345, 54543, 54545, 54565, 54567, 56543, 56545, 56565, 56567, 56765, 56767, 56787, 56789, 65454, 65654, 65678, 67654, 67656, 67676, 67678, 67876, 67878, 76543, 76545, 76565, 76567, 76765, 76767, 76787, 76789, 78765, 78767, 78787, 78789, 78987, 78989, 87654, 87676, 87678, 87878, 87898, 89876, 89878, 89898, 98765, 98767, 98787, 98789, 98987, 98989, 101010, 101012, 121210, 123212, 123232, 123234, 123432, 123454, 123456, 210101, 210121, 212101, 212123, 212321, 212323, 212343, 212345, 232101, 232121, 232123, 232321, 232323, 232343, 232345, 234321, 234323, 234343, 234345, 234543, 234545, 234565, 234567, 321010, 321210, 321212, 321234, 323232, 323454, 343210, 343212, 343434, 343454, 345454, 345456, 345654, 345656, 345676, 345678, 432101, 432121, 432123, 432321, 432323, 432343, 432345, 434321, 434323, 434343, 434345, 434543, 434545, 434565, 434567, 454321, 454323, 454343, 454345, 454543, 454545, 454565, 454567, 456543, 456545, 456565, 456567, 456765, 456767, 456787, 456789, 543210, 543212, 543234, 543432, 543434, 543454, 543456, 545432, 545654, 545656, 545676, 545678, 565432, 565434, 565454, 565456, 565654, 565676, 565678, 567654, 567678, 567878, 654321.

Some larger examples :