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junction n.  and  palindromic n.

First numbers that belong to both sets:

101, 111, 202, 212, 303, 313, 404, 414, 505, 515, 606, 616, 707, 717, 808, 818, 909, 919, 1001, 2002, 3003, 4004, 5005, 6006, 7007, 8008, 9009, 10001, 11111, 11311, 11511, 11711, 11911, 12221, 12421, 12621, 12821, 20002, 21112, 21312, 21512, 21712, 21912, 22222, 22422, 22622, 22822, 30003, 31113, 31313, 31513, 31713, 31913, 32223, 32423, 32623, 32823, 40004, 41114, 41314, 41514, 41714, 41914, 42224, 42424, 42624, 42824, 50005, 51115, 51315, 51515, 51715, 51915, 52225, 52425, 52625, 52825, 60006, 61116, 61316, 61516, 61716, 61916, 62226, 62426, 62626, 62826, 70007, 71117, 71317, 71517, 71717, 71917, 72227, 72427, 72627, 72827, 80008, 81118, 81318, 81518, 81718, 81918, 82228, 82428, 82628, 82828, 90009, 91119, 91319, 91519, 91719, 91919, 92229, 92429, 92629, 92829, 100001, 120021, 121121, 122221, 123321, 124421, 125521, 126621, 127721, 128821, 129921, 200002, 220022, 221122, 222222, 223322, 224422, 225522, 226622, 227722, 228822, 229922, 300003, 320023, 321123, 322223, 323323, 324423, 325523, 326623, 327723, 328823, 329923, 400004, 420024, 421124, 422224, 423324, 424424, 425524, 426624, 427724, 428824, 429924, 500005, 520025, 521125, 522225, 523325, 524425, 525525, 526625, 527725, 528825, 529925, 600006, 620026, 621126, 622226, 623326, 624426, 625526, 626626, 627726, 628826, 629926, 700007, 720027, 721127, 722227, 723327, 724427, 725527, 726627, 727727, 728827, 729927, 800008, 820028, 821128, 822228, 823328, 824428, 825528, 826628, 827728, 828828, 829928, 900009, 920029, 921129, 922229, 923329, 924429, 925529, 926629, 927729, 928829, 929929, 1000001, 1101011, 1103011, 1105011, 1107011, 1109011, 1111111, 1113111, 1115111, 1117111, 1121211, 1123211, 1125211, 1131311, 1133311, 1141411, 1200021, 1201021, 1203021, 1204021, 1205021, 1206021, 1207021, 1208021, 1210121, 1212121, 1214121, 1216121, 1218121, 1220221, 1222221, 1224221, 1226221, 1228221, 1230321, 1232321, 1234321, 1236321, 1238321, 1240421, 1242421, 1244421, 1246421, 1248421, 1250521, 1252521, 1254521, 1256521, 1258521, 1260621, 1262621, 1264621, 1266621, 1270721, 1272721, 1274721, 1280821, 1282821, 1290921, 1300031, 1302031, 1304031, 1306031, 1308031.

Some larger examples :