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palindromic n.  and  Ulam n.

First numbers that belong to both sets:

1, 2, 3, 4, 6, 8, 11, 77, 99, 131, 282, 363, 414, 434, 585, 646, 949, 2112, 2332, 2552, 2662, 5335, 5665, 8008, 8338, 8668, 10501, 13531, 13931, 15251, 16961, 17071, 18381, 18581, 18681, 22122, 22322, 23632, 23932, 25452, 26962, 28582, 28682, 30703, 30803, 32123, 32423, 33633, 34043, 35253, 35553, 37173, 38283, 39793, 40504, 42324, 43634, 45254, 45454, 47074, 48384, 48684, 49794, 50505, 53935, 55555, 56965, 58585, 59795, 60806, 65256, 67176, 68586, 69796, 69996, 72127, 73937, 75157, 75257, 75457, 76967, 77077, 78287, 79997, 80408, 80708, 81918, 82428, 86668, 87178, 88288, 89798, 90709, 90809, 92329, 94049, 95159, 96969, 97079, 99799, 101101, 106601, 118811, 119911, 154451, 166661, 167761, 172271, 206602, 211112, 241142, 242242, 246642, 258852, 260062, 309903, 316613, 398893, 403304, 420024, 421124, 433334, 437734, 450054, 468864, 473374, 486684, 506605, 513315, 524425, 525525, 529925, 543345, 561165, 572275, 577775, 611116, 652256, 664466, 665566, 683386, 694496, 703307, 704407, 715517, 733337, 756657, 768867, 786687, 787787, 807708, 825528, 826628, 837738, 844448, 856658, 861168, 862268, 873378, 878878, 891198, 892298, 896698, 900009, 912219, 978879, 984489, 1026201, 1046401, 1058501, 1069601, 1073701, 1074701, 1081801, 1086801, 1097901, 1178711, 1186811, 1198911, 1202021, 1210121, 1222221, 1230321, 1242421, 1302031, 1306031, 1310131, 1311131, 1331331, 1334331, 1338331, 1342431, 1351531, 1407041, 1423241, 1426241, 1434341, 1442441, 1443441, 1462641, 1490941, 1494941, 1498941, 1538351, 1539351, 1555551, 1574751, 1582851, 1583851, 1591951, 1598951, 1611161, 1659561, 1687861, 1695961, 1699961, 1723271, 1731371, 1735371, 1751571, 1800081, 1803081, 1804081, 1807081, 1811181, 1815181, 1819181, 1823281, 1827281, 1831381, 1839381, 1843481, 1847481, 1860681, 1871781, 1904091, 1919191, 1927291, 1928291, 1967691, 1971791, 1975791, 1979791, 1983891, 2054502, 2066602, 2069602, 2085802, 2094902, 2110112, 2194912, 2202022, 2210122, 2222222, 2226222, 2242422, 2262622, 2306032, 2314132, 2315132, 2318132, 2334332, 2342432, 2366632, 2407042, 2423242, 2426242, 2427242, 2435342, 2438342, 2451542, 2455542, 2463642, 2466642, 2470742, 2490942, 2494942, 2555552, 2574752, 2575752.

Some larger examples :