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arithmetic n.  and  metadrome

First numbers that belong to both sets:

1, 3, 5, 6, 7, 13, 14, 15, 17, 19, 23, 27, 29, 35, 37, 38, 39, 45, 46, 47, 49, 56, 57, 59, 67, 68, 69, 78, 79, 89, 123, 125, 126, 127, 129, 134, 135, 137, 138, 139, 145, 147, 149, 157, 158, 159, 167, 168, 169, 179, 189, 235, 236, 237, 238, 239, 245, 246, 247, 248, 249, 257, 258, 259, 267, 269, 278, 345, 347, 348, 349, 356, 357, 358, 359, 367, 369, 378, 379, 389, 456, 457, 459, 467, 469, 478, 479, 489, 568, 569, 579, 589, 678, 679, 689, 789, 1235, 1237, 1238, 1239, 1245, 1246, 1247, 1248, 1249, 1257, 1259, 1267, 1268, 1269, 1278, 1279, 1289, 1345, 1347, 1349, 1356, 1357, 1358, 1367, 1369, 1379, 1389, 1457, 1459, 1469, 1478, 1479, 1489, 1567, 1569, 1578, 1579, 1589, 1678, 1679, 1689, 1789, 2345, 2346, 2347, 2348, 2349, 2357, 2358, 2359, 2367, 2369, 2379, 2389, 2457, 2459, 2467, 2468, 2469, 2478, 2479, 2489, 2567, 2568, 2569, 2579, 2589, 2678, 2679, 2689, 2789, 3457, 3458, 3459, 3467, 3469, 3478, 3479, 3489, 3567, 3569, 3579, 3589, 3678, 3679, 3689, 4567, 4569, 4578, 4579, 4589, 4678, 4679, 4689, 4789, 5678, 5689, 5789, 6789, 12345, 12347, 12349, 12356, 12357, 12358, 12359, 12367, 12369, 12378, 12379, 12389, 12457, 12459, 12467, 12469, 12478, 12479, 12489, 12567, 12569, 12578, 12579, 12589, 12678, 12679, 12689, 12789, 13457, 13458, 13459, 13467, 13469, 13478, 13479, 13489, 13567, 13568, 13569, 13578, 13579, 13589, 13678, 13679, 13789, 14567, 14568, 14569, 14579, 14678, 14679, 14689, 14789, 15678, 15679, 15689, 15789, 16789, 23457, 23459, 23467, 23468, 23469, 23478, 23479, 23489, 23567, 23569, 23579, 23589, 23678, 23679, 23689, 23789, 24567, 24569, 24589, 24678, 24679, 24689, 24789, 25678, 25679, 25689, 25789.

Some larger examples :