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balanced n.  and  esthetic n.

First numbers that belong to both sets:

10, 12, 21, 56, 78, 210, 212, 232, 434, 565, 654, 676, 678, 787, 789, 898, 1210, 2343, 3432, 6767, 8765, 8987, 8989, 9878, 9898, 10121, 12123, 12321, 12343, 21234, 34545, 43210, 43434, 45432, 45454, 45654, 45676, 54323, 54343, 54565, 210121, 212101, 232101, 232323, 234321, 234567, 321010, 323210, 323454, 343432, 343434, 345656, 432321, 434343, 543454, 545654, 567676, 654345, 654543, 656765, 676565, 678787, 678789, 678987, 678989, 789878, 878787, 878789, 987678, 987876, 2121232, 2123454, 2321010, 2321012, 2321234, 2323232, 2345432, 2345456, 2345656, 2345676, 3232121, 3232343, 3234343, 3234567, 3432321, 3434321, 3434543, 3454345, 3454545, 3456545, 4323210, 4323234, 4543232, 5432121, 5434343, 5434545, 5454343, 5454345, 5654343, 5656545, 5678987, 5678989, 6543234, 6565432, 6565678, 6765456, 6789876, 7654565, 7878765, 7878987, 8767678, 8787678, 8787898, 8789876, 9876565, 9876787, 9878787, 9878789, 9878989, 9898767, 10123434, 12101210, 12101212, 12101234, 12121234, 12123232, 12123456, 12343232, 12345454, 12345654, 12345678, 34321210, 34321212, 34545434, 34565432, 34565654, 34565676, 34567876, 43210123, 43212101, 43212323, 43232345, 43234343, 43234567, 43432101, 43432323, 43434343, 43434543, 43454345, 43456543, 43456567, 45432323, 45434321, 45434545, 45434565, 45454545, 45456545, 45656545, 45676565, 54321210, 54321212, 54343234, 54343432, 54343456, 54567678, 56543432, 56543456, 56545432, 56545456, 56545676, 56567878, 56765654, 56765676, 56767676, 56767898, 56787678, 56787898, 56789876, 65432321, 65454343, 65676565.