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palindromic n.  and  self n.

First numbers that belong to both sets:

1, 3, 5, 7, 9, 121, 222, 323, 424, 525, 626, 727, 828, 929, 1111, 2112, 3113, 4114, 5115, 6116, 7117, 8118, 9119, 10401, 11211, 12921, 13731, 14541, 15351, 16161, 18881, 19691, 20402, 21212, 22922, 23732, 24542, 25352, 26162, 28882, 29692, 30403, 31213, 32923, 33733, 34543, 35353, 36163, 38883, 39693, 40404, 41214, 42924, 43734, 44544, 45354, 46164, 48884, 49694, 50405, 51215, 52925, 53735, 54545, 55355, 56165, 58885, 59695, 60406, 61216, 62926, 63736, 64546, 65356, 66166, 68886, 69696, 70407, 71217, 72927, 73737, 74547, 75357, 76167, 78887, 79697, 80408, 81218, 82928, 83738, 84548, 85358, 86168, 88888, 89698, 90409, 91219, 92929, 93739, 94549, 95359, 96169, 98889, 99699, 102201, 111111, 139931, 148841, 157751, 166661, 175571, 184481, 193391, 202202, 211112, 239932, 248842, 257752, 266662, 275572, 284482, 293392, 302203, 311113, 339933, 348843, 357753, 366663, 375573, 384483, 393393, 402204, 411114, 439934, 448844, 457754, 466664, 475574, 484484, 493394, 502205, 511115, 539935, 548845, 557755, 566665, 575575, 584485, 593395, 602206, 611116, 639936, 648846, 657756, 666666, 675576, 684486, 693396, 702207, 711117, 739937, 748847, 757757, 766667, 775577, 784487, 793397, 802208, 811118, 839938, 848848, 857758, 866668, 875578, 884488, 893398, 902209, 911119, 939939, 948849, 957759, 966669, 975579, 984489, 993399, 1006001, 1012101, 1020201, 1039301, 1047401, 1055501, 1063601, 1071701, 1098901, 1104011, 1110111, 1129211, 1137311, 1145411, 1153511, 1161611, 1188811, 1196911, 1217121, 1219121, 1225221, 1227221, 1233321, 1235321, 1241421, 1243421, 1251521, 1278721, 1286821, 1294921, 1307031, 1315131, 1323231, 1331331, 1358531, 1366631, 1368631, 1374731, 1376731, 1382831, 1384831, 1390931, 1392931, 1405041, 1413141, 1421241, 1448441, 1456541, 1464641, 1472741, 1480841, 1499941, 1503051, 1511151, 1538351, 1546451, 1554551, 1562651, 1570751, 1589851, 1597951, 1601061, 1628261, 1636361, 1644461, 1652561, 1660661, 1679761, 1687861, 1695961, 1718171, 1726271, 1734371, 1742471, 1750571, 1769671, 1777771, 1785871, 1793971, 1808081, 1816181, 1824281, 1832381, 1840481, 1859581, 1867681, 1875781, 1883881, 1891981, 1906091, 1914191, 1922291, 1930391, 1949491, 1957591.

Some larger examples :