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lucky n.  and  nialpdrome

First numbers that belong to both sets:

1, 3, 7, 9, 21, 31, 33, 43, 51, 63, 73, 75, 87, 93, 99, 111, 211, 321, 331, 421, 433, 511, 541, 553, 621, 631, 643, 651, 655, 741, 777, 831, 841, 855, 873, 883, 885, 931, 933, 961, 975, 981, 991, 993, 997, 2211, 2221, 3111, 4321, 4431, 4441, 4443, 5211, 5433, 5551, 6111, 6211, 6331, 6411, 6433, 6531, 6541, 6553, 6621, 6631, 6661, 6663, 7111, 7311, 7321, 7333, 7443, 7531, 7533, 7551, 7633, 7711, 7755, 8221, 8331, 8421, 8551, 8553, 8611, 8641, 8655, 8661, 8773, 8833, 8841, 8871, 9211, 9331, 9421, 9441, 9543, 9555, 9621, 9631, 9643, 9661, 9663, 9733, 9751, 9753, 9775, 9811, 9841, 9883, 9961, 9985, 9987, 9997, 9999, 21111, 33211, 33333, 42211, 43333, 44311, 44421, 55555, 63111, 63321, 64221, 64333, 64441, 65431, 65521, 65551, 65553, 66433, 66543, 66553, 66661, 72211, 73221, 74221, 74311, 74331, 74433, 75111, 75211, 75421, 75433, 75441, 75511, 76533, 76551, 76555, 76633, 76663, 77211, 77431, 77521, 77533, 77553, 77653, 77661, 77721, 77733, 77763, 81111, 82111, 84331, 84411, 84421, 85333, 85441, 85555, 86221, 86331, 86421, 86631, 86661, 87111, 87411, 87433, 87633, 87721, 87733, 87741, 87751, 88221, 88333, 88441, 88521, 88551, 88653, 88663, 88665, 88755, 88773, 88821, 88851, 88861, 88881, 91111, 92211, 94221, 94321, 94443, 95431, 96211, 96333, 96411, 96553, 96621, 96631, 96663, 97411, 97443, 97531, 97555, 97743, 97755, 98443, 98511, 98553, 98611, 98661, 98731, 98755, 98763, 98871, 98877, 99211, 99333, 99531, 99541, 99543, 99555, 99753, 99843, 99855, 99865, 99877, 99885, 99921, 99955, 99973, 99987, 111111, 321111, 332211, 333321, 433221, 443221, 522111, 542221, 552111, 554431, 555411, 555421, 642211, 644211, 644221, 644331, 644431, 644433, 652221, 654111, 654433, 655333, 655431, 655441, 655521, 663111, 663331, 664221, 664411, 664431, 665331, 665421, 665553, 666111, 666333, 666421, 666511, 666541.

Some larger examples :