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Cunningham n.  and  plaindrome

First numbers that belong to both sets:

3, 5, 7, 8, 9, 15, 17, 24, 26, 28, 33, 35, 37, 48, 99, 122, 124, 126, 127, 129, 145, 168, 224, 226, 244, 255, 257, 288, 344, 399, 577, 677, 899, 999, 1155, 1157, 1224, 1226, 1368, 1445, 1599, 2499, 3599, 4488, 4899, 5777, 6888, 7777, 7999, 9999, 11235, 11237, 11448, 13455, 13457, 13688, 16899, 22499, 25599, 26999, 27888, 28899, 33488, 39999, 89999, 99999, 111555, 111557, 112224, 112226, 113568, 115599, 122499, 124999, 134688, 136899, 146688, 159999, 224677, 249999, 344568, 359999, 444888, 448899, 489999, 688899, 999999, 1123599, 1144899, 1157777, 1345599, 1368899, 1689999, 2249999, 2559999, 2666688, 2778888, 2788899, 2889999, 3348899, 3999999, 7999999, 8999999, 9999999, 11115555, 11115557, 11122224, 11122226, 11135568, 11155599, 11222499, 11336688, 11356899, 11444688, 11559999, 12249999, 13446888, 13468899, 13689999, 14668899, 15999999, 23357888, 24999999, 26999999, 34456899, 35999999, 44448888, 44488899, 44889999, 48999999, 68889999, 99999999, 112359999, 114489999, 122677777, 124999999, 134559999, 136889999, 168999999, 224999999, 255999999, 266668899, 277788888, 277888899, 278889999, 288999999, 334889999, 399999999, 899999999, 999999999, 1111155555, 1111155557, 1111222224, 1111222226, 1111355568, 1111555599, 1112222499, 1113356688, 1113556899, 1115559999, 1122249999, 1133466888, 1133668899, 1135689999, 1144468899, 1155999999, 1224999999, 1279999999, 1344468888, 1344688899, 1346889999, 1368999999, 1466889999, 1599999999, 2335788899, 2499999999, 3445689999, 3599999999, 4444488888, 4444888899, 4448889999, 4488999999, 4899999999, 6888999999, 7999999999, 9999999999, 11122233445, 11235999999, 11448999999, 13455999999, 13688999999, 15666777888, 16899999999, 22499999999, 25599999999, 26666889999, 26999999999, 27777888888, 27778888899, 27788889999, 27888999999, 28899999999, 33488999999, 39999999999, 89999999999, 99999999999, 111111555555, 111111555557, 111112222224, 111112222226, 111113555568, 111115555599, 111122222499, 111133556688, 111135556899, 111155559999, 111222249999, 111333666888, 111335668899, 111355689999, 111555999999, 112224999999, 113344668888, 113346688899, 113366889999, 113568999999, 114446889999, 115599999999, 122499999999, 124999999999, 134444688888, 134446888899, 134468889999, 134688999999, 136899999999, 146688999999, 159999999999, 233578889999, 249999999999, 344568999999, 359999999999, 444444888888, 444448888899, 444488889999, 444888999999, 448899999999, 489999999999, 688899999999, 999999999999, 1123599999999, 1144899999999, 1345599999999, 1368899999999, 1566677788899, 1689999999999, 2249999999999, 2559999999999, 2666688999999, 2777778888888, 2777788888899, 2777888889999, 2778888999999, 2788899999999, 2889999999999, 3348899999999, 3999999999999, 7999999999999, 8999999999999, 9999999999999, 11111115555555, 11111115555557, 11111122222224, 11111122222226, 11111135555568, 11111155555599, 11111222222499, 11111335556688, 11111355556899, 11111555559999, 11112222249999.

Some larger examples :