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happy n.  and  Zuckerman n.

First numbers that belong to both sets:

1, 7, 1112, 1115, 1184, 1212, 1332, 1575, 2112, 3132, 3312, 8112, 11232, 11328, 12132, 12312, 13212, 13248, 13824, 14112, 16632, 18432, 21132, 21184, 21312, 21672, 22176, 23112, 23424, 26136, 26712, 27216, 31212, 32112, 32616, 34272, 35175, 38112, 41112, 42432, 66312, 81312, 111216, 111432, 111612, 112116, 113292, 113715, 114312, 116112, 119232, 121116, 121392, 121932, 123264, 126432, 132192, 134112, 136224, 139212, 141312, 143112, 161112, 162432, 163296, 179424, 192132, 193212, 211116, 213192, 219132, 219744, 221616, 231264, 231336, 232128, 232416, 239112, 241632, 261216, 266112, 293112, 312336, 313632, 314112, 316224, 321192, 336312, 341112, 411312, 413112, 421632, 431112, 611112, 613332, 621216, 626112, 662112, 731115, 921132, 941472, 1111111, 1111112, 1111115, 1111212, 1112112, 1112224, 1113264, 1116432, 1117935, 1121112, 1124112, 1131264, 1132416, 1141248, 1141632, 1142112, 1143216, 1197315, 1211112, 1214112, 1221472, 1222112, 1241136, 1242112, 1271424, 1282112, 1311264, 1312416, 1323648, 1341216, 1346112, 1364112, 1371195, 1378944, 1411632, 1412112, 1413216, 1421136, 1422112, 1431216, 1433376, 1436112, 1461312, 1472128, 1482112, 1634112, 1641312, 1711115, 1711395, 1812224, 1882112, 1886976, 1911735, 1983744, 2111112, 2112128, 2114112, 2117248, 2118144, 2122112, 2141136, 2141184, 2142112, 2192832, 2212112, 2214112, 2218112, 2224128, 2228224, 2282112, 2291328, 2333772, 2343168, 2382912, 2411136, 2612736, 2673216, 2772224, 2794176, 2822144, 2832192, 2842112, 3111264, 3112416, 3134376, 3141216, 3146112, 3164112, 3186432, 3234816, 3322944, 3411216, 3416112, 3614112, 3618432, 3639168, 3798144, 4111632, 4111744, 4112112, 4112128, 4113216, 4121136, 4122112, 4131216, 4136112, 4136832, 4161312, 4211136, 4212224, 4218112, 4282112, 4311216, 4313736, 4316112, 4611312, 6132672, 6134112, 6141312, 6314112, 6411312, 6422976, 6441984, 6838272, 7111272, 7112224, 7131915, 7217112, 7811328, 7881216, 8112128, 8122112, 8142336, 8182272, 8218112, 8232192, 8332416, 8423424, 9173115.