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modest n.  and  nialpdrome

First numbers that belong to both sets:

111, 211, 222, 311, 333, 411, 422, 433, 444, 511, 533, 555, 611, 622, 633, 654, 666, 711, 721, 733, 763, 777, 811, 822, 833, 844, 866, 872, 888, 911, 933, 981, 999, 1111, 2111, 2222, 3111, 3333, 4111, 4222, 4333, 4444, 5111, 5333, 5555, 6111, 6222, 6333, 6666, 7111, 7333, 7777, 8111, 8222, 8333, 8444, 8666, 8888, 9111, 9333, 9999, 11111, 21111, 22111, 22222, 31111, 32111, 32222, 33111, 33333, 41111, 42111, 42222, 43111, 43333, 44111, 44222, 44333, 44444, 51111, 52111, 52222, 53111, 53333, 54111, 54222, 54333, 55111, 55333, 55555, 61111, 62111, 62222, 63111, 63333, 64111, 64222, 64333, 64432, 64444, 65111, 65333, 65555, 66111, 66222, 66333, 66666, 71111, 72111, 72222, 73111, 73333, 74111, 74222, 74333, 75111, 75333, 75555, 76111, 76222, 76333, 76444, 76666, 77111, 77333, 77777, 81111, 82111, 82222, 83111, 83333, 84111, 84222, 84333, 84444, 85111, 85333, 85555, 86111, 86222, 86333, 86666, 87111, 87333, 88111, 88222, 88333, 88444, 88666, 88888, 91111, 92111, 92222, 93111, 93333, 94111, 94222, 94333, 95111, 95333, 95555, 96111, 96222, 96333, 96432, 96444, 96666, 97111, 97333, 98111, 98222, 98333, 98441, 98666, 98777, 98882, 99111, 99333, 99999, 111111, 211111, 221111, 222222, 311111, 321111, 322222, 331111, 333333, 411111, 421111, 422222, 431111, 433333, 441111, 442222, 443333, 444444, 511111, 521111, 522222, 531111, 533333, 541111, 542222, 543333, 551111, 553333, 555555, 611111, 621111, 622222, 631111, 633333, 641111, 642222, 643333, 644444, 651111, 653333, 655555, 661111, 662222, 663333, 666666, 711111, 721111, 722222, 731111, 733333, 741111, 742222, 743333, 751111, 753333, 755555, 761111, 762222, 763333, 764444, 766666, 771111, 773333, 777777, 811111, 821111, 822222, 831111, 833333, 841111, 842222, 843333, 844444, 851111, 853333, 855555, 861111, 862222, 863333, 866666, 871111, 873333, 881111, 882222, 883333, 884444, 886666, 888888, 911111, 921111, 922222, 931111, 933333, 941111, 942222, 943333, 951111, 953333, 955555, 961111, 962222.

Some larger examples :