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apocalyptic n.  and  arithmetic n.

First numbers that belong to both sets:

157, 220, 222, 224, 245, 247, 251, 278, 285, 286, 287, 355, 361, 366, 382, 390, 411, 434, 443, 478, 497, 499, 506, 539, 540, 541, 564, 580, 582, 583, 612, 614, 620, 635, 646, 647, 649, 660, 662, 667, 669, 671, 686, 693, 702, 714, 718, 723, 747, 748, 749, 787, 807, 820, 822, 823, 824, 826, 836, 838, 840, 846, 857, 859, 861, 864, 865, 869, 871, 875, 884, 894, 920, 924, 929, 931, 937, 977, 979, 983, 985, 994, 1002, 1004, 1019, 1026, 1031, 1056, 1060, 1062, 1065, 1081, 1086, 1087, 1102, 1103, 1105, 1128, 1133, 1135, 1139, 1140, 1141, 1155, 1157, 1158, 1162, 1166, 1191, 1194, 1199, 1212, 1217, 1219, 1230, 1240, 1241, 1243, 1245, 1246, 1247, 1257, 1259, 1261, 1265, 1267, 1270, 1271, 1277, 1279, 1281, 1285, 1286, 1289, 1290, 1298, 1301, 1303, 1305, 1310, 1316, 1318, 1321, 1333, 1338, 1339, 1340, 1341, 1343, 1345, 1347, 1349, 1351, 1374, 1382, 1399, 1403, 1411, 1415, 1416, 1420, 1421, 1422, 1424, 1429, 1434, 1435, 1438, 1449, 1465, 1470, 1478, 1482, 1483, 1485, 1487, 1493, 1494, 1495, 1497, 1499, 1501, 1503, 1510, 1515, 1527, 1535, 1539, 1541, 1550, 1556, 1561, 1562, 1565, 1572, 1574, 1578, 1589, 1590, 1591, 1611, 1623, 1625, 1626, 1627, 1628, 1630, 1631, 1633, 1634, 1638, 1639, 1644, 1651, 1652, 1653, 1656, 1661, 1663, 1665, 1667, 1669, 1670, 1674, 1679, 1687, 1695, 1713, 1715, 1722, 1723, 1739, 1743, 1744, 1750, 1751, 1753, 1755, 1758, 1760, 1766, 1769, 1772, 1774, 1775, 1777, 1783, 1784, 1785, 1797, 1798, 1803, 1804, 1805, 1806, 1807, 1809, 1811, 1813, 1817, 1819, 1820, 1821, 1823, 1827, 1829, 1831, 1833, 1837, 1839, 1843, 1849, 1851, 1853, 1855, 1857, 1860, 1862, 1866, 1868.

Some larger examples :