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gapful n.  and  Zuckerman n.

First numbers that belong to both sets:

132, 135, 315, 1111, 1212, 1296, 1332, 1344, 1575, 2112, 3276, 4224, 4416, 6144, 11112, 11115, 11172, 11232, 11424, 12132, 12312, 12432, 13212, 13248, 13272, 13932, 14112, 16128, 16416, 16632, 17115, 17136, 18432, 18816, 21216, 21728, 23424, 24112, 32616, 32832, 34272, 35175, 38112, 51975, 61824, 77175, 91728, 111111, 111132, 111135, 111168, 111195, 111216, 111312, 111315, 111432, 111612, 111915, 112224, 112416, 113112, 113115, 113292, 113328, 113616, 113715, 114192, 114312, 114432, 114816, 114912, 116112, 116172, 117264, 117432, 117824, 117936, 118272, 119115, 119232, 121392, 121932, 122112, 123732, 124416, 126432, 131112, 131115, 131328, 131712, 132192, 134112, 139212, 139968, 141192, 141216, 141312, 141912, 143112, 146112, 149112, 161112, 161136, 162432, 163296, 164112, 167328, 171612, 177135, 177184, 179424, 182112, 182784, 183168, 183312, 189216, 191115, 192132, 193212, 194112, 196128, 211112, 219744, 221184, 221232, 222112, 231264, 234432, 241472, 244224, 266112, 282624, 311115, 312336, 313416, 313632, 314112, 316116, 338112, 344736, 371175, 381312, 383616, 411648, 413112, 417312, 434112, 437472, 442368, 476112, 612864, 628224, 719712, 732312, 772632, 914112, 973728, 1111212, 1111968, 1112112, 1112232, 1112832, 1113912, 1114176, 1116432, 1117935, 1118112, 1119312, 1121112, 1121232, 1121616, 1122192, 1122312, 1122336, 1122432, 1122816, 1122912, 1123632, 1124112, 1126272, 1127112, 1131192, 1131732, 1132128, 1132416, 1134432, 1141632, 1142112, 1143216, 1143744, 1161216, 1161972, 1166112, 1167264, 1168128, 1171212, 1173312, 1181376, 1181712, 1191132, 1191915, 1193616, 1194912, 1197315, 1211112, 1211232, 1211328, 1211616, 1212192, 1212312, 1212912, 1214112, 1217664, 1218432, 1218816, 1221192, 1221216, 1221312, 1221912, 1222144, 1223112, 1223712, 1226112, 1229112, 1231272, 1231632, 1232112, 1233792, 1238112, 1241136, 1247232, 1262112, 1263168, 1264896, 1266192, 1271424, 1274112, 1277136, 1281216, 1281312, 1282176, 1283328, 1292112, 1294272, 1311744, 1312128, 1312416, 1312632, 1313172, 1314432, 1319112, 1319328, 1322112, 1323216, 1323648, 1329696, 1337112, 1341216, 1346112, 1347192, 1349136, 1361232, 1362312, 1364112, 1371132, 1371195, 1372224, 1373715, 1378272, 1378944, 1382112, 1389312, 1411632, 1411992, 1412112, 1413216, 1418112, 1421136, 1427328, 1431216.

Some larger examples :