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arithmetic n.  and  modest n.

First numbers that belong to both sets:

13, 19, 23, 29, 39, 46, 49, 59, 69, 79, 89, 103, 109, 111, 133, 199, 203, 206, 209, 211, 222, 233, 266, 299, 309, 311, 327, 399, 406, 409, 411, 418, 422, 433, 499, 509, 511, 515, 533, 545, 555, 599, 609, 611, 618, 622, 627, 633, 654, 699, 709, 721, 733, 763, 777, 799, 809, 811, 812, 822, 824, 833, 836, 899, 911, 933, 999, 1003, 1009, 1011, 1015, 1022, 1027, 1030, 1033, 1037, 1045, 1055, 1099, 1111, 1133, 1199, 1218, 1222, 1227, 1233, 1244, 1254, 1266, 1299, 1333, 1339, 1399, 1421, 1422, 1433, 1442, 1463, 1477, 1499, 1527, 1533, 1545, 1555, 1599, 1622, 1624, 1633, 1644, 1672, 1699, 1733, 1751, 1799, 1822, 1827, 1833, 1854, 1866, 1881, 1933, 1957, 1999, 2003, 2006, 2009, 2022, 2027, 2030, 2033, 2036, 2037, 2045, 2054, 2055, 2060, 2090, 2099, 2111, 2127, 2133, 2163, 2177, 2199, 2222, 2233, 2266, 2333, 2369, 2399, 2427, 2433, 2436, 2444, 2454, 2472, 2488, 2499, 2533, 2545, 2555, 2599, 2633, 2639, 2666, 2678, 2699, 2733, 2781, 2799, 2833, 2863, 2877, 2899, 2933, 2987, 2999, 3009, 3027, 3037, 3045, 3054, 3055, 3066, 3081, 3090, 3099, 3111, 3133, 3193, 3199, 3233, 3236, 3248, 3266, 3296, 3299, 3333, 3399, 3451, 3499, 3545, 3555, 3563, 3577, 3599, 3644, 3654, 3666, 3699, 3799, 3857, 3899, 3999, 4006, 4009, 4012, 4027, 4037, 4045, 4054, 4055, 4060, 4066, 4074, 4088, 4099, 4111, 4148, 4199, 4222, 4254, 4263, 4266, 4277, 4299, 4333, 4399, 4444, 4466, 4499, 4555, 4581, 4669, 4699, 4799, 4854, 4866, 4872, 4888, 4899, 4963, 4999, 5009, 5015, 5027, 5037, 5045, 5055, 5075, 5099, 5111, 5135, 5185, 5199, 5278, 5299, 5333, 5399, 5466, 5481, 5499, 5555, 5599, 5663, 5677, 5684, 5688, 5699, 5799.

Some larger examples :