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apocalyptic n.  and  Ulam n.

First numbers that belong to both sets:

243, 382, 390, 434, 497, 612, 624, 646, 720, 800, 820, 861, 864, 866, 927, 983, 1018, 1081, 1103, 1155, 1157, 1164, 1191, 1230, 1257, 1338, 1340, 1465, 1470, 1472, 1492, 1550, 1682, 1792, 1812, 1853, 1919, 1944, 1946, 1968, 2012, 2032, 2034, 2054, 2095, 2115, 2117, 2134, 2247, 2252, 2254, 2327, 2330, 2445, 2447, 2462, 2464, 2511, 2550, 2552, 2572, 2574, 2581, 2589, 2618, 2628, 2630, 2635, 2674, 2721, 2723, 2748, 2762, 2789, 2809, 2814, 2816, 2833, 2899, 2921, 2985, 2987, 3029, 3031, 3038, 3041, 3065, 3131, 3207, 3217, 3219, 3236, 3239, 3261, 3263, 3288, 3305, 3368, 3371, 3373, 3390, 3393, 3454, 3481, 3483, 3495, 3525, 3605, 3608, 3610, 3622, 3630, 3649, 3671, 3691, 3696, 3698, 3725, 3740, 3759, 3762, 3806, 3808, 3872, 3874, 3886, 3930, 3952, 3960, 3962, 3974, 3991, 4018, 4040, 4057, 4101, 4121, 4148, 4150, 4155, 4165, 4167, 4187, 4211, 4233, 4258, 4260, 4294, 4326, 4341, 4343, 4363, 4365, 4368, 4370, 4390, 4392, 4407, 4409, 4451, 4453, 4470, 4517, 4519, 4578, 4580, 4619, 4622, 4624, 4641, 4644, 4666, 4668, 4707, 4729, 4798, 4800, 4878, 4883, 4900, 4903, 4905, 4925, 4927, 4969, 4971, 5018, 5020, 5035, 5037, 5049, 5052, 5059, 5079, 5081, 5096, 5118, 5159, 5162, 5164, 5184, 5208, 5250, 5252, 5269, 5272, 5274, 5291, 5294, 5296, 5318, 5335, 5357, 5382, 5384, 5484, 5487, 5489, 5514, 5516, 5531, 5533, 5550, 5597, 5663, 5665, 5685, 5768, 5770, 5795, 5797, 5812, 5814, 5826, 5856, 5858, 5875, 5878, 5880, 5895, 5900, 6024, 6027, 6029, 6049, 6051, 6068, 6107, 6110, 6112, 6134, 6154, 6176, 6239, 6242, 6244, 6283, 6310, 6322, 6325, 6327, 6352, 6354, 6366, 6391, 6393, 6410, 6418, 6420, 6435, 6457, 6459, 6479, 6481, 6520, 6523, 6567, 6569, 6586, 6633.

Some larger examples :