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hoax n.  and  nialpdrome

First numbers that belong to both sets:

22, 84, 85, 94, 644, 650, 654, 660, 663, 732, 762, 855, 860, 861, 922, 985, 1111, 5332, 5422, 6500, 6531, 6600, 6620, 6633, 7650, 7762, 8420, 8421, 8600, 8653, 8720, 8754, 8851, 9330, 9333, 9540, 9630, 9650, 9652, 9711, 9742, 9772, 9843, 9861, 9940, 9942, 9985, 43222, 44331, 44420, 44442, 52222, 63330, 63332, 63333, 65000, 65542, 66000, 66200, 66540, 66555, 66640, 66651, 76320, 76332, 76440, 76443, 76500, 76522, 76531, 77422, 77442, 77532, 77752, 82220, 83322, 84200, 84433, 85533, 86000, 86433, 86520, 86540, 86553, 86620, 86622, 86631, 86652, 87200, 87322, 87332, 87522, 88540, 88650, 88732, 88842, 88850, 88852, 88863, 93300, 94444, 95400, 95422, 95433, 96300, 96500, 96620, 96660, 97222, 98554, 98653, 98655, 98730, 98850, 98853, 99400, 99444, 99650, 99652, 99742, 99860, 99985, 433332, 442220, 444200, 444411, 544441, 554433, 633300, 643332, 644332, 650000, 655411, 660000, 662000, 664320, 665400, 665433, 666400, 666553, 666652, 754321, 763200, 764400, 764444, 765000, 765532, 765552, 773322, 775310, 775440, 775540, 776511, 776520, 776641, 776644, 776660, 777621, 777644, 822200, 842000, 843322, 843332, 844411, 853222, 855220, 855444, 855532, 855553, 860000, 862110, 864222, 864321, 865200, 865220, 865311, 865400, 865431, 865432, 865540, 866200, 872000, 874220, 875542, 876541, 876550, 877221, 877422, 877522, 877542, 877620, 877630, 877711, 877774, 885400, 885440, 885444, 886420, 886500, 886533, 887530, 887550, 887775, 888331, 888500, 888642, 888774, 888820, 933000, 944311, 944320, 944420, 952222, 954000, 955332, 955432, 963000, 964311, 965000, 965433, 965510, 965532, 966200, 966511, 966532, 966541, 966550, 966600, 966630, 973111, 974444, 976440, 976522, 977422, 977622, 977732, 985441, 985522, 985550, 986521, 986611, 986650, 987300, 987754, 988411, 988431, 988500, 988722, 988764, 988850, 992211, 993210, 993330, 994000, 995422, 996210, 996310, 996420, 996421, 996500, 996620, 997222, 997620, 997762, 998420, 998554, 998600, 998610, 998830, 999320, 999650, 999860, 4422200, 4433332, 4442000, 5433210, 5544333, 5553333, 5554432, 6333000.

Some larger examples :