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odious n.  and  Zuckerman n.

First numbers that belong to both sets:

1, 2, 4, 7, 8, 11, 112, 115, 128, 224, 672, 1113, 1116, 1184, 1296, 1311, 1332, 1344, 1715, 2144, 2232, 4416, 7112, 8832, 11111, 11112, 11115, 11172, 11232, 11424, 11711, 12112, 12128, 12216, 12224, 18112, 19116, 21112, 21184, 21312, 22144, 24112, 24912, 32112, 33111, 34992, 37212, 41112, 41616, 42624, 42912, 43632, 48128, 61344, 62112, 64128, 71232, 71316, 73332, 77175, 81216, 82944, 83232, 86112, 89712, 91728, 111212, 111264, 111424, 112116, 113184, 113292, 113319, 113328, 114112, 114312, 116112, 116172, 116316, 117432, 118144, 119115, 119232, 119313, 121116, 121716, 121932, 122112, 123732, 131112, 131115, 131712, 134112, 134136, 139968, 141192, 141216, 141312, 141912, 143112, 144128, 146112, 147112, 161112, 161136, 162432, 167328, 175175, 177135, 179424, 182784, 183168, 189216, 192132, 193212, 196128, 211116, 211176, 212224, 214144, 218112, 219132, 231336, 232128, 232416, 239112, 241472, 241632, 244224, 282112, 282624, 291168, 294192, 312336, 312732, 316116, 316224, 317184, 317331, 321192, 331317, 331344, 333315, 341112, 341712, 371112, 373212, 381312, 382464, 411112, 411216, 411712, 414112, 416112, 421888, 437472, 438912, 441216, 441312, 442112, 476112, 613332, 621216, 662112, 671328, 688128, 698112, 711312, 711872, 713664, 719712, 721112, 731115, 732312, 733131, 733824, 742112, 772632, 817712, 863136, 918144, 921132, 964224, 973728, 1111113, 1111116, 1111131, 1111173, 1111311, 1111344, 1111416, 1111712, 1112128, 1112232, 1112272, 1112616, 1113111, 1114176, 1116432, 1121112, 1121232, 1122192, 1122624, 1123632, 1124112, 1124224, 1127196, 1128448, 1131111, 1131264, 1131711, 1132128, 1132224, 1132416, 1134144, 1134432, 1142112, 1143216, 1143744, 1164288, 1168128, 1169316, 1171212, 1173312, 1177176, 1177911, 1182272, 1191915, 1194912, 1197315, 1211112, 1212112, 1213344, 1214112, 1216128, 1217916, 1218112, 1221192, 1221216, 1221312, 1222112, 1223112, 1223424, 1223712, 1231272, 1242112, 1261824, 1263168, 1264896, 1266192, 1274112, 1277136, 1283328, 1292112, 1311111, 1311744, 1312128, 1312224, 1312632, 1313172, 1323216, 1331424, 1337112, 1339416, 1341216, 1349136, 1364112, 1372224, 1373715, 1378272, 1382112, 1389312, 1411112, 1412112, 1412224, 1413216, 1421136, 1421824, 1422112, 1427328.

Some larger examples :