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arithmetic n.  and  untouchable n.

First numbers that belong to both sets:

5, 96, 188, 206, 210, 238, 246, 248, 262, 276, 304, 322, 326, 342, 406, 426, 430, 474, 498, 518, 540, 552, 612, 658, 668, 670, 708, 714, 718, 726, 748, 750, 766, 782, 836, 852, 894, 902, 926, 934, 966, 982, 996, 1002, 1028, 1046, 1060, 1068, 1074, 1078, 1102, 1128, 1146, 1148, 1150, 1162, 1180, 1212, 1222, 1246, 1248, 1254, 1266, 1288, 1316, 1318, 1326, 1342, 1380, 1388, 1398, 1406, 1420, 1422, 1438, 1506, 1508, 1510, 1528, 1542, 1566, 1578, 1632, 1650, 1716, 1718, 1758, 1766, 1774, 1806, 1820, 1822, 1830, 1838, 1842, 1844, 1860, 1866, 1888, 1894, 1896, 1958, 1972, 1986, 1992, 2010, 2022, 2024, 2036, 2058, 2062, 2068, 2078, 2108, 2118, 2128, 2148, 2158, 2168, 2174, 2190, 2198, 2226, 2228, 2232, 2262, 2302, 2322, 2324, 2338, 2364, 2366, 2376, 2408, 2422, 2430, 2436, 2446, 2454, 2464, 2484, 2490, 2496, 2502, 2514, 2518, 2530, 2564, 2568, 2586, 2588, 2590, 2606, 2614, 2718, 2724, 2726, 2758, 2760, 2766, 2774, 2784, 2788, 2828, 2850, 2856, 2874, 2876, 2894, 2902, 2914, 2922, 2946, 2950, 2968, 2982, 2994, 2996, 3018, 3036, 3060, 3078, 3102, 3126, 3132, 3142, 3144, 3156, 3162, 3174, 3186, 3198, 3228, 3234, 3236, 3238, 3246, 3266, 3270, 3278, 3296, 3306, 3318, 3340, 3356, 3366, 3378, 3384, 3402, 3406, 3422, 3428, 3430, 3432, 3448, 3454, 3476, 3486, 3510, 3524, 3580, 3588, 3590, 3604, 3630, 3642, 3652, 3666, 3670, 3682, 3738, 3752, 3758, 3774, 3786, 3788, 3792, 3808, 3812, 3818, 3820, 3828, 3832, 3860, 3862, 3876, 3902, 3936, 3940, 3942, 3954, 3958, 3974, 3982, 4026, 4046, 4062, 4070, 4078, 4086, 4088, 4098, 4104, 4120, 4148, 4170, 4172, 4190, 4198, 4206, 4216, 4238, 4268, 4296, 4302, 4304, 4308, 4316, 4318, 4320.

Some larger examples :