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junction n.  and  Zuckerman n.

First numbers that belong to both sets:

111, 115, 212, 216, 315, 612, 816, 1112, 1116, 3312, 4416, 6624, 7112, 8832, 11111, 11115, 11212, 11313, 11711, 12112, 12312, 12712, 13113, 13212, 13311, 13824, 14112, 17115, 18112, 21112, 21312, 23112, 28416, 31113, 31212, 31311, 32112, 33111, 37212, 38112, 41112, 42624, 81312, 111112, 111312, 112416, 113112, 114624, 114816, 122112, 124112, 131112, 131712, 136224, 141216, 141824, 142112, 146112, 164112, 182112, 212112, 214112, 218112, 221112, 244224, 248832, 282624, 311112, 316224, 371112, 411216, 412112, 414112, 416112, 434112, 441312, 614112, 628224, 711312, 741216, 772632, 929232, 973728, 1111111, 1111113, 1111115, 1111117, 1111212, 1111311, 1111416, 1111424, 1112112, 1113111, 1114112, 1117935, 1118112, 1121112, 1122624, 1122816, 1124224, 1127112, 1131111, 1141112, 1171212, 1211112, 1212224, 1218432, 1221216, 1222112, 1223424, 1226112, 1242112, 1247232, 1261824, 1262112, 1264128, 1281216, 1311111, 1331424, 1378944, 1393119, 1411112, 1412224, 1421824, 1422112, 1442112, 1612224, 1622112, 1711115, 1711416, 1733319, 1784832, 1811328, 1812224, 1818624, 1876224, 1911735, 1983744, 2111112, 2116224, 2119932, 2121216, 2122112, 2126112, 2127216, 2142112, 2162112, 2192832, 2211216, 2212112, 2214112, 2216112, 2228224, 2231424, 2234112, 2241312, 2332224, 2342112, 2379132, 2416128, 2421312, 2473632, 2612112, 2716224, 2719332, 2772224, 2927232, 2939328, 3111111, 3117933, 3124224, 3128832, 3131424, 3172932, 3186432, 3242112, 3311424, 3412224, 3422112, 3618432, 3712128, 3771432, 3798144, 4111112, 4122112, 4132224, 4136832, 4144128, 4221312, 4242432, 4271232, 4272128, 4322112, 4741632, 4914432, 6122112, 6212112, 6642432, 6931332, 7111111, 7112112, 7131117, 7167132, 7463232, 7711424, 7811328, 8116224, 8121216, 8231424, 8312832, 8368128, 8831232, 9126432, 9191232, 11111112, 11112216, 11112224, 11116224, 11121216, 11122112, 11124112, 11126112, 11127424, 11142112, 11162112, 11167632, 11171328, 11172224, 11181216, 11184128, 11211216, 11212112, 11214112, 11216112, 11221112, 11231424, 11234112, 11241312, 11261112, 11272128, 11324112, 11329632, 11332224, 11341824, 11342112, 11344128, 11394432, 11412112, 11414112, 11421312, 11432112, 11442432, 11444224, 11491632, 11612112, 11621112, 11641728, 11711112, 11791332, 11826432, 11891232, 11912832, 12111216, 12111424, 12112112, 12114112, 12116112, 12121112, 12124416, 12134112, 12141312, 12161112, 12211112, 12212224, 12222112, 12242112, 12311424, 12314112, 12344832, 12411312.

Some larger examples :