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arithmetic n.  and  Zuckerman n.

First numbers that belong to both sets:

1, 3, 5, 6, 7, 11, 15, 111, 115, 132, 135, 212, 224, 315, 432, 612, 672, 735, 1111, 1113, 1115, 1131, 1212, 1311, 1416, 1715, 2144, 2232, 3111, 3132, 3168, 3171, 3915, 6624, 7112, 7119, 8832, 9612, 11111, 11112, 11115, 11232, 11313, 11331, 11424, 11711, 11872, 12128, 12712, 12768, 13113, 13272, 13311, 13824, 14144, 16224, 16416, 16632, 17115, 19116, 21112, 21216, 21672, 21728, 22112, 22176, 23112, 24192, 26712, 27132, 31131, 31311, 32172, 32616, 33264, 34272, 34992, 37212, 38112, 41232, 42112, 42336, 42432, 43632, 51975, 61344, 61824, 62112, 64128, 66312, 81312, 86112, 89712, 92232, 93744, 111111, 111112, 111115, 111135, 111195, 111212, 111264, 111272, 111315, 111432, 111612, 111915, 112224, 112416, 113115, 113184, 113292, 113319, 113616, 113715, 114312, 114816, 114912, 116112, 116316, 117264, 117432, 118112, 119115, 119313, 121344, 121392, 121716, 122112, 126432, 131112, 131115, 131139, 131424, 131712, 131733, 132192, 134112, 136224, 139212, 141112, 141184, 141216, 141312, 143112, 147112, 161136, 162432, 163296, 167328, 171115, 171612, 172116, 173313, 175175, 177135, 179424, 182112, 191115, 196128, 211112, 211176, 212112, 213192, 214112, 214144, 217112, 219744, 221232, 222112, 229392, 231264, 231336, 232416, 241632, 242112, 261216, 266112, 282112, 291168, 293112, 311115, 311328, 311472, 312732, 313173, 313416, 316116, 317331, 321192, 331317, 331344, 338112, 341712, 344736, 371112, 371175, 411112, 411192, 411216, 411264, 411312, 411648, 411912, 412112, 413112, 413184, 416112, 418112, 421888, 422112, 422144, 431112, 431136, 437472, 438912, 441216, 441312, 476112, 491112, 511175, 611112, 612864, 614112, 621216, 628224, 647136, 711312, 717115, 719712, 721112, 731115, 732312, 733131, 741216, 742112, 817712, 843264, 911115, 911736, 929232, 941472, 964224, 972216, 973728, 1111111, 1111115, 1111117, 1111131, 1111173, 1111212, 1111311, 1111968, 1112232, 1117935, 1118112, 1119312, 1121112, 1122312, 1122432, 1122912, 1124112, 1124224, 1126272, 1127112, 1131111, 1131711, 1132128, 1134432, 1141112, 1141632, 1142112, 1161216, 1161972, 1167264, 1169316, 1171212, 1173312, 1177176, 1181184.

Some larger examples :