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amenable n.  and  zygodrome

First numbers that belong to both sets:

33, 44, 77, 88, 333, 444, 777, 888, 1100, 1133, 1144, 1177, 1188, 2200, 2233, 2244, 2277, 2288, 3300, 3333, 3344, 3377, 3388, 4400, 4433, 4444, 4477, 4488, 5500, 5533, 5544, 5577, 5588, 6600, 6633, 6644, 6677, 6688, 7700, 7733, 7744, 7777, 7788, 8800, 8833, 8844, 8877, 8888, 9900, 9933, 9944, 9977, 9988, 11000, 11100, 11133, 11144, 11177, 11188, 11333, 11444, 11777, 11888, 22000, 22200, 22233, 22244, 22277, 22288, 22333, 22444, 22777, 22888, 33000, 33300, 33333, 33344, 33377, 33388, 33444, 33777, 33888, 44000, 44333, 44400, 44433, 44444, 44477, 44488, 44777, 44888, 55000, 55333, 55444, 55500, 55533, 55544, 55577, 55588, 55777, 55888, 66000, 66333, 66444, 66600, 66633, 66644, 66677, 66688, 66777, 66888, 77000, 77333, 77444, 77700, 77733, 77744, 77777, 77788, 77888, 88000, 88333, 88444, 88777, 88800, 88833, 88844, 88877, 88888, 99000, 99333, 99444, 99777, 99888, 99900, 99933, 99944, 99977, 99988, 110000, 110033, 110044, 110077, 110088, 111000, 111100, 111133, 111144, 111177, 111188, 111333, 111444, 111777, 111888, 112200, 112233, 112244, 112277, 112288, 113300, 113333, 113344, 113377, 113388, 114400, 114433, 114444, 114477, 114488, 115500, 115533, 115544, 115577, 115588, 116600, 116633, 116644, 116677, 116688, 117700, 117733, 117744, 117777, 117788, 118800, 118833, 118844, 118877, 118888, 119900, 119933, 119944, 119977, 119988, 220000, 220033, 220044, 220077, 220088, 221100, 221133, 221144, 221177, 221188, 222000, 222200, 222233, 222244, 222277, 222288, 222333, 222444, 222777, 222888, 223300, 223333, 223344, 223377, 223388, 224400, 224433, 224444, 224477, 224488, 225500, 225533, 225544, 225577, 225588, 226600, 226633, 226644, 226677, 226688, 227700, 227733, 227744, 227777, 227788, 228800, 228833, 228844, 228877, 228888, 229900, 229933, 229944, 229977, 229988, 330000, 330033, 330044, 330077, 330088, 331100, 331133, 331144, 331177, 331188, 332200, 332233, 332244, 332277, 332288, 333000, 333300, 333333, 333344, 333377, 333388, 333444, 333777, 333888, 334400, 334433, 334444, 334477, 334488, 335500, 335533.

Some larger examples :