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arithmetic n.  and  self n.

First numbers that belong to both sets:

1, 3, 5, 7, 20, 31, 42, 53, 86, 97, 110, 132, 143, 154, 165, 187, 198, 209, 211, 222, 233, 255, 266, 277, 299, 310, 323, 334, 345, 356, 367, 378, 389, 411, 413, 435, 446, 457, 479, 501, 547, 558, 569, 580, 591, 602, 613, 615, 637, 659, 670, 681, 692, 703, 714, 716, 727, 749, 771, 782, 793, 815, 817, 839, 861, 883, 894, 905, 918, 929, 940, 951, 973, 995, 1006, 1021, 1032, 1043, 1054, 1065, 1076, 1087, 1109, 1111, 1122, 1133, 1155, 1166, 1177, 1188, 1199, 1212, 1223, 1245, 1267, 1278, 1289, 1311, 1313, 1335, 1357, 1379, 1390, 1401, 1412, 1414, 1436, 1447, 1469, 1491, 1502, 1513, 1515, 1526, 1537, 1559, 1581, 1592, 1603, 1614, 1627, 1638, 1649, 1660, 1671, 1693, 1704, 1715, 1717, 1739, 1750, 1761, 1772, 1783, 1794, 1805, 1829, 1851, 1862, 1873, 1895, 1917, 1919, 1941, 1963, 1974, 1985, 2022, 2033, 2055, 2077, 2099, 2110, 2123, 2134, 2145, 2156, 2167, 2189, 2211, 2213, 2224, 2235, 2246, 2257, 2279, 2301, 2347, 2358, 2369, 2380, 2391, 2413, 2415, 2437, 2459, 2470, 2481, 2492, 2503, 2514, 2516, 2527, 2538, 2549, 2571, 2582, 2593, 2615, 2617, 2639, 2661, 2683, 2694, 2705, 2718, 2729, 2740, 2751, 2773, 2784, 2795, 2806, 2819, 2830, 2841, 2852, 2863, 2874, 2885, 2907, 2918, 2931, 2942, 2953, 2975, 3023, 3045, 3067, 3078, 3089, 3111, 3113, 3124, 3135, 3157, 3168, 3179, 3190, 3201, 3212, 3214, 3236, 3247, 3269, 3291, 3302, 3313, 3315, 3326, 3337, 3359, 3381, 3403, 3414, 3416, 3427, 3438, 3449, 3460, 3471, 3493, 3515, 3517, 3539, 3550, 3561, 3572, 3583, 3594, 3605, 3618, 3629, 3640, 3651, 3662, 3673, 3695, 3717, 3719, 3741, 3752, 3763, 3774, 3785, 3818, 3820, 3831, 3853, 3864.

Some larger examples :