Search a number
apocalyptic n.  and  balanced n.

First numbers that belong to both sets:

226, 278, 312, 384, 434, 508, 528, 539, 541, 578, 582, 583, 612, 614, 620, 624, 647, 660, 662, 666, 684, 714, 787, 820, 824, 838, 841, 842, 844, 850, 865, 866, 868, 894, 898, 920, 929, 970, 1102, 1138, 1202, 1298, 1394, 1470, 1478, 1490, 1634, 1670, 1758, 1766, 1914, 1946, 2054, 2070, 2079, 2095, 2103, 2134, 2155, 2157, 2158, 2163, 2170, 2206, 2222, 2226, 2227, 2229, 2234, 2247, 2251, 2254, 2259, 2262, 2265, 2275, 2277, 2278, 2281, 2284, 2290, 2292, 2296, 2319, 2327, 2331, 2333, 2343, 2347, 2349, 2358, 2361, 2362, 2364, 2382, 2386, 2387, 2389, 2390, 2396, 2403, 2409, 2410, 2430, 2443, 2445, 2446, 2454, 2460, 2467, 2469, 2470, 2473, 2501, 2530, 2532, 2566, 2575, 2586, 2589, 2603, 2605, 2606, 2614, 2618, 2620, 2635, 2637, 2638, 2643, 2646, 2649, 2659, 2665, 2668, 2674, 2676, 2678, 2680, 2699, 2701, 2702, 2709, 2710, 2714, 2716, 2723, 2725, 2726, 2730, 2738, 2755, 2757, 2762, 2764, 2766, 2769, 2770, 2792, 2823, 2826, 2835, 2837, 2841, 2842, 2844, 2854, 2857, 2858, 2860, 2865, 2866, 2868, 2872, 2882, 2883, 2890, 2898, 2900, 2910, 2914, 2926, 2928, 2930, 2947, 2949, 2950, 2953, 2954, 2956, 2962, 2964, 2980, 2984, 2992, 3009, 3010, 3012, 3016, 3024, 3040, 3101, 3115, 3117, 3118, 3126, 3129, 3130, 3132, 3143, 3149, 3150, 3155, 3157, 3158, 3161, 3162, 3164, 3171, 3173, 3177, 3186, 3188, 3192, 3207, 3211, 3213, 3219, 3221, 3225, 3228, 3238, 3242, 3244, 3249, 3250, 3256, 3267, 3269, 3270, 3273, 3274, 3276, 3281, 3282, 3284, 3288, 3297, 3298, 3300, 3304, 3312, 3339, 3342, 3350, 3354, 3356, 3363, 3365, 3366, 3369, 3370, 3377, 3380, 3384, 3398, 3402, 3409, 3412, 3416, 3426, 3428, 3432, 3459, 3461, 3462, 3465, 3480, 3490, 3492.

Some larger examples :