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arithmetic n.  and  happy n.

First numbers that belong to both sets:

1, 7, 13, 19, 23, 31, 44, 49, 68, 70, 79, 86, 91, 94, 97, 103, 109, 129, 133, 139, 167, 188, 190, 193, 203, 219, 230, 236, 239, 262, 263, 280, 291, 293, 301, 302, 310, 313, 319, 326, 329, 331, 356, 365, 367, 376, 379, 383, 391, 397, 404, 409, 446, 464, 469, 478, 487, 563, 565, 566, 608, 617, 622, 623, 632, 635, 637, 638, 644, 649, 653, 655, 665, 671, 673, 683, 694, 709, 716, 736, 739, 748, 761, 763, 790, 793, 806, 820, 833, 836, 860, 863, 874, 881, 899, 901, 907, 910, 912, 913, 921, 923, 931, 932, 937, 940, 946, 973, 989, 998, 1003, 1009, 1029, 1030, 1033, 1039, 1067, 1076, 1093, 1115, 1121, 1122, 1125, 1128, 1141, 1148, 1151, 1158, 1177, 1182, 1185, 1188, 1209, 1211, 1212, 1215, 1218, 1221, 1222, 1233, 1247, 1257, 1275, 1277, 1281, 1285, 1288, 1290, 1299, 1303, 1309, 1323, 1330, 1333, 1335, 1337, 1339, 1353, 1366, 1373, 1390, 1393, 1411, 1427, 1447, 1457, 1474, 1475, 1478, 1481, 1484, 1487, 1511, 1512, 1518, 1527, 1528, 1533, 1547, 1557, 1572, 1574, 1578, 1581, 1582, 1599, 1607, 1663, 1670, 1679, 1697, 1717, 1724, 1725, 1727, 1733, 1742, 1744, 1745, 1748, 1755, 1758, 1760, 1769, 1771, 1772, 1784, 1785, 1796, 1814, 1815, 1821, 1841, 1844, 1847, 1851, 1857, 1880, 1881, 1888, 1902, 1903, 1929, 1933, 1959, 1967, 1992, 1995, 2003, 2019, 2030, 2036, 2039, 2062, 2063, 2091, 2093, 2109, 2111, 2115, 2118, 2121, 2133, 2147, 2151, 2157, 2158, 2174, 2175, 2177, 2181, 2185, 2190, 2199, 2206, 2211, 2221, 2224, 2242, 2245, 2254, 2257, 2260, 2285, 2309, 2313, 2333, 2338, 2339, 2369, 2383, 2390, 2393, 2396, 2417, 2422, 2455, 2457, 2471, 2478.

Some larger examples :