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odious n.  and  zygodrome

First numbers that belong to both sets:

11, 22, 44, 55, 88, 333, 555, 666, 1144, 1166, 1177, 1199, 2211, 2255, 2288, 3311, 3333, 3355, 3388, 3399, 4411, 4422, 4433, 4455, 5511, 5566, 5577, 5588, 6622, 6655, 6666, 6699, 7711, 7722, 7744, 7777, 8811, 8822, 8844, 8855, 8866, 8877, 9900, 9911, 9944, 9966, 9977, 9988, 11111, 11166, 11199, 11222, 11444, 11555, 11666, 11777, 11888, 11999, 22222, 22233, 22255, 22277, 22299, 22444, 22555, 22777, 22888, 33000, 33111, 33311, 33322, 33344, 33377, 33444, 33666, 44111, 44333, 44411, 44444, 44466, 44477, 44888, 44999, 55000, 55222, 55333, 55444, 55544, 55555, 55588, 55666, 55777, 55888, 66000, 66222, 66333, 66622, 66633, 66644, 66677, 66688, 66777, 66888, 66999, 77000, 77222, 77444, 77555, 77666, 77711, 77744, 77788, 77999, 88111, 88222, 88555, 88666, 88777, 88811, 88822, 88833, 88888, 88899, 88999, 99000, 99333, 99444, 99666, 99777, 99922, 99933, 99944, 99955, 99977, 99988, 110000, 110044, 110066, 110077, 110088, 110099, 111100, 111122, 111133, 111144, 111155, 111199, 111444, 111888, 111999, 112222, 112255, 112266, 112299, 113300, 113333, 113355, 113366, 113388, 113399, 114411, 114422, 114433, 114488, 114499, 115522, 115533, 115555, 115588, 116611, 116644, 116666, 116688, 117700, 117722, 117733, 117755, 117766, 117777, 117799, 118800, 118822, 118833, 118866, 118877, 118888, 118899, 119900, 119922, 119933, 119944, 119955, 119977, 119988, 220000, 220033, 220088, 220099, 221122, 221133, 221155, 221188, 222200, 222211, 222244, 222266, 222288, 222333, 222555, 222888, 222999, 223300, 223322, 223333, 223355, 223388, 224411, 224444, 224455, 225511, 225544, 225555, 225577, 225588, 226600, 226611, 226655, 226666, 226699, 227700, 227733, 227744, 227788, 227799, 228811, 228822, 228844, 228855, 228866, 228877, 228899, 229944, 229955, 229988, 330000, 330022, 330033, 330066, 330077, 330088, 330099, 331100, 331122, 331133, 331144, 331155, 331177, 331188, 332200, 332211, 332255, 332266, 332299, 333000, 333222, 333311, 333322, 333355, 333366, 333377, 333444, 333555, 333666, 333888, 334411, 334422, 334444, 334455, 334466, 334477.

Some larger examples :