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pernicious n.  and  zygodrome

First numbers that belong to both sets:

11, 22, 33, 44, 55, 66, 88, 333, 555, 666, 1144, 1166, 1177, 1199, 2211, 2255, 2288, 3333, 3355, 3388, 3399, 4411, 4422, 4433, 4455, 5511, 5577, 5588, 6655, 6666, 6699, 7722, 7744, 7777, 8811, 8822, 8844, 8855, 8866, 8877, 9900, 9944, 9988, 11199, 11444, 11555, 11666, 11777, 11888, 11999, 22255, 22277, 22555, 22888, 33000, 33111, 33311, 33322, 33344, 33377, 33444, 33666, 44411, 44477, 44999, 55222, 55333, 55444, 55555, 55588, 55888, 66000, 66222, 66333, 66622, 66633, 66644, 66677, 66688, 66777, 66888, 77000, 77444, 77555, 77711, 77788, 88555, 88811, 88822, 88833, 88999, 99000, 99333, 99444, 99666, 99777, 99922, 99944, 99977, 99988, 110044, 110066, 110077, 110088, 111100, 111122, 111144, 111199, 111888, 111999, 112222, 112255, 112299, 113333, 113355, 113366, 113388, 113399, 114411, 114422, 114488, 114499, 115522, 115588, 116666, 117722, 117733, 117755, 117766, 117777, 118800, 118822, 118833, 118866, 118888, 119933, 119944, 220088, 220099, 221122, 221133, 221155, 221188, 222200, 222211, 222244, 222288, 222333, 222555, 222999, 223300, 223355, 224411, 224444, 224455, 225511, 225544, 226611, 226655, 226666, 226699, 227700, 227733, 227788, 227799, 228811, 228822, 228844, 228877, 228899, 229944, 229955, 229988, 330000, 330022, 330033, 330066, 330088, 331133, 331144, 332200, 332255, 332299, 333000, 333311, 333322, 333377, 333444, 333555, 333888, 334455, 334466, 335511, 335533, 335566, 335577, 335599, 336688, 337711, 337755, 337788, 338855, 338899, 339922, 339933, 339944, 339955, 440033, 440077, 440099, 441144, 441155, 441188, 442211, 442244, 442266, 442277, 443322, 443366, 443377, 444400, 444422, 444433, 444488, 444666, 445533, 445555, 446600, 446699, 447711, 447722, 447744, 448811, 448822, 448888, 449944, 449966, 449977, 449988, 550000, 550022, 550033, 550088, 551166, 551177, 551188, 552200, 552299, 553311, 553399, 554411, 554422, 554488, 555500, 555511, 555522, 555599, 556622, 556633, 556655, 557700, 557722, 557733, 557766, 557777, 558800, 558866, 558888, 559944, 660000, 660044, 660066, 660099, 661111, 661122, 661199, 662266, 662288, 663311, 663388.

Some larger examples :