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alternating n.  and  Harshad n.

First numbers that belong to both sets:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 21, 27, 30, 36, 45, 50, 54, 63, 70, 72, 81, 90, 210, 216, 230, 234, 252, 270, 410, 414, 432, 450, 476, 612, 630, 690, 810, 832, 870, 874, 1010, 1012, 1014, 1016, 1032, 1050, 1056, 1090, 1092, 1098, 1212, 1230, 1232, 1236, 1270, 1272, 1274, 1278, 1296, 1410, 1416, 1450, 1452, 1456, 1458, 1476, 1494, 1630, 1632, 1638, 1652, 1656, 1674, 1692, 1810, 1812, 1818, 1836, 1854, 1872, 1890, 1896, 1898, 3012, 3030, 3032, 3036, 3038, 3070, 3072, 3078, 3096, 3210, 3216, 3250, 3252, 3258, 3276, 3290, 3294, 3416, 3430, 3432, 3438, 3456, 3472, 3474, 3492, 3610, 3612, 3616, 3618, 3636, 3654, 3672, 3690, 3696, 3816, 3834, 3852, 3870, 5010, 5016, 5050, 5052, 5054, 5056, 5058, 5076, 5094, 5230, 5232, 5238, 5256, 5274, 5292, 5410, 5412, 5418, 5432, 5436, 5454, 5472, 5490, 5496, 5616, 5632, 5634, 5652, 5670, 5810, 5814, 5832, 5850, 5856, 5876, 7030, 7032, 7038, 7056, 7070, 7072, 7074, 7092, 7210, 7212, 7216, 7218, 7236, 7254, 7272, 7290, 7296, 7416, 7434, 7452, 7470, 7614, 7632, 7650, 7656, 7812, 7830, 7872, 9010, 9012, 9018, 9036, 9054, 9072, 9090, 9096, 9212, 9216, 9232, 9234, 9252, 9270, 9414, 9432, 9450, 9456, 9612, 9630, 9672, 9810, 9816, 9854, 9856, 10101, 10107, 10109, 10125, 10143, 10161, 10185, 10305, 10307, 10309, 10323, 10341, 10365, 10503, 10505, 10521, 10543, 10545, 10701, 10703, 10725, 10727, 10787, 10901, 10905, 10963, 10983, 10989, 12103, 12105, 12123, 12141, 12165, 12181, 12303, 12321, 12345, 12369, 12501, 12525, 12563, 12705, 12747, 12987, 14103, 14121, 14145, 14301, 14325, 14383, 14385, 14505, 14521, 14705, 14725, 14763, 14769, 14927, 14985, 16101, 16125, 16149, 16169, 16305, 16389, 16527, 16541, 16583, 16767.

Some larger examples :