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Curzon n.  and  balanced n.

First numbers that belong to both sets:

2, 9, 21, 41, 50, 78, 114, 141, 153, 165, 198, 209, 210, 278, 410, 426, 438, 534, 558, 590, 614, 618, 653, 690, 713, 714, 789, 806, 809, 810, 818, 849, 866, 894, 905, 930, 1014, 1070, 1110, 1178, 1190, 1346, 1394, 1398, 1454, 1478, 1730, 1758, 1766, 1778, 1790, 2109, 2141, 2169, 2253, 2261, 2361, 2393, 2394, 2406, 2430, 2454, 2501, 2505, 2529, 2538, 2589, 2613, 2618, 2661, 2666, 2673, 2690, 2709, 2738, 2778, 2786, 2790, 2826, 2829, 2841, 2858, 2889, 2910, 2913, 2930, 2961, 3101, 3149, 3150, 3158, 3161, 3186, 3213, 3225, 3273, 3281, 3350, 3354, 3366, 3401, 3473, 3474, 3521, 3605, 3606, 3609, 3621, 3626, 3653, 3654, 3665, 3666, 3729, 3845, 3849, 3858, 6881, 7025, 7041, 7193, 7361, 7433, 7445, 7469, 7841, 7865, 7929, 7953, 8069, 8169, 8213, 8309, 8345, 8381, 8414, 8441, 8481, 8510, 8553, 8558, 8601, 8649, 8666, 8745, 8798, 8813, 8918, 8945, 8961, 8969, 8985, 8990, 9006, 9038, 9065, 9066, 9074, 9114, 9125, 9126, 9170, 9185, 9213, 9225, 9269, 9293, 9374, 9398, 9401, 9429, 9434, 9449, 9458, 9518, 9525, 9578, 9650, 9785, 9830, 9869, 9881, 9906, 9926, 9930, 9998, 10005, 10010, 10025, 10053, 10058, 10130, 10178, 10241, 10253, 10281, 10358, 10373, 10469, 10473, 10481, 10505, 10509, 10550, 10553, 10574, 10581, 10610, 10613, 10638, 10661, 10673, 10698, 10749, 10781, 10805, 10806, 10830, 10841, 10893, 10901, 10929, 11033, 11045, 11046, 11078, 11085, 11129, 11141, 11145, 11153, 11190, 11265, 11309, 11310, 11318, 11321, 11345, 11349, 11354, 11369, 11370, 11405, 11429, 11430, 11453, 11513, 11558, 11565, 11594, 11601, 11613, 11666, 11729, 11765, 11769, 11790, 11801, 11813, 11814, 11870, 11873, 11909, 11913, 12038, 12041, 12066, 12098, 12125, 12249, 12285, 12381, 12410, 12425, 12461, 12485, 12489, 12494, 12506, 12518.

Some larger examples :