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alternating n.  and  balanced prime

First numbers that belong to both sets:

5, 563, 947, 2903, 2963, 6323, 6367, 8747, 12547, 12583, 14543, 14747, 16567, 16787, 16987, 18341, 30103, 34543, 38183, 52529, 52727, 56149, 58129, 58543, 74567, 76561, 90703, 92363, 92581, 96763, 212903, 218143, 218749, 230143, 234727, 236707, 252163, 252341, 254383, 254747, 256307, 270749, 270967, 292561, 292921, 294347, 294787, 414521, 418927, 418987, 432343, 432743, 454507, 456523, 458701, 458987, 470501, 494743, 498301, 614729, 616507, 616723, 630181, 632147, 634307, 636547, 650543, 652747, 654967, 656147, 672181, 672943, 674941, 676129, 676727, 676987, 692963, 694367, 810547, 810763, 810967, 812387, 816329, 816341, 818347, 830789, 832963, 834143, 836707, 852763, 858763, 876581, 878743, 878783, 890963, 892321, 896167, 896347, 896543, 1016783, 1018987, 1058921, 1072763, 1076587, 1090303, 1092307, 1094963, 1098121, 1212703, 1212787, 1214743, 1218709, 1238521, 1250189, 1250749, 1250923, 1254541, 1258343, 1272163, 1276123, 1298161, 1298747, 1414703, 1430921, 1432583, 1436363, 1436387, 1438103, 1450747, 1452181, 1452323, 1458343, 1472743, 1472987, 1476967, 1478369, 1610963, 1610981, 1632121, 1638701, 1650563, 1650589, 1650763, 1654567, 1654727, 1672301, 1674587, 1674901, 1678349, 1678921, 1692709, 1694723, 1694909, 1834321, 1836943, 1850969, 1872301, 1872569, 1876163, 1876309, 1878187, 1878769, 1894381, 1898563, 3010123, 3010523, 3012907, 3032363, 3036589, 3038747, 3050141, 3052769, 3052943, 3056341, 3056387, 3058927, 3070547, 3074587, 3078743, 3090187, 3090301, 3092723, 3094303, 3210307, 3212323, 3232387, 3236963, 3238127, 3252961, 3258149, 3258569, 3270343, 3292343, 3296581, 3410989, 3412741, 3412987, 3414343, 3414707, 3416521, 3416747, 3416767, 3418901, 3430907, 3436309, 3436507, 3450743, 3452143, 3456743, 3494363, 3494923, 3494969, 3614969, 3614987, 3616901, 3630923, 3632303, 3634343, 3634789, 3634907, 3650567, 3652367, 3658129, 3670763, 3674767, 3676129, 3676187, 3678347, 3678943, 3698963, 3810503, 3810523, 3810727, 3812183, 3814703, 3816383, 3816581, 3830909, 3834547, 3836501, 3838123, 3854723, 3854749, 3856549, 3858749, 3870703, 3870947, 3872767, 3876161, 3876787, 3878107, 3878767, 3890323, 3894181, 3896323, 3896363, 5010367, 5012141, 5018929, 5032507, 5058107, 5058583, 5058721, 5058743, 5070509, 5070727, 5072329, 5076587, 5092921, 5092943, 5092961, 5092987, 5096387, 5098987, 5212561, 5214947, 5230963, 5232323, 5232749, 5236949.

Some larger examples :