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ABA n.  and  odious n.

First numbers that belong to both sets:

8, 32, 50, 64, 81, 98, 128, 162, 200, 242, 324, 375, 392, 512, 578, 648, 722, 800, 896, 968, 1024, 1029, 1058, 1250, 1568, 1682, 1922, 2048, 2178, 2187, 2312, 2450, 2500, 2592, 2888, 3000, 3042, 3200, 3362, 3698, 3872, 4232, 4374, 4802, 5000, 5184, 5202, 6050, 6272, 6728, 6962, 7688, 8192, 8232, 8450, 8712, 8978, 9248, 9604, 9800, 10082, 10368, 11250, 11552, 11858, 12168, 12482, 12800, 13448, 14450, 14792, 15138, 15488, 15625, 15842, 16384, 16562, 16928, 17496, 18050, 18818, 19208, 20000, 20402, 20577, 20808, 21218, 22528, 24000, 24200, 25088, 25538, 26912, 27378, 27848, 29282, 30752, 31250, 32258, 32768, 33282, 33800, 34322, 34848, 35912, 36450, 36992, 38642, 39200, 40000, 40328, 40898, 41472, 42050, 43218, 44402, 45000, 46208, 46818, 47432, 48672, 49298, 49928, 51200, 53138, 53792, 55778, 57122, 57800, 58564, 59049, 59168, 59858, 60552, 61250, 61952, 63368, 64082, 65522, 65856, 66248, 67712, 68450, 71442, 72200, 73167, 74498, 75272, 76832, 77618, 80000, 80802, 81608, 82944, 83232, 84872, 87362, 92450, 94178, 96800, 99458, 100352, 101250, 102152, 103058, 104882, 106496, 106722, 107648, 109512, 110450, 111392, 114242, 114244, 114688, 117128, 118098, 122018, 123008, 125000, 126002, 128625, 129032, 131072, 132098, 133128, 134162, 135200, 137288, 138338, 139392, 139968, 142578, 143648, 145800, 146882, 147968, 151250, 151959, 153664, 154568, 155682, 156800, 160178, 161312, 162450, 163592, 164616, 165888, 168200, 172872, 176418, 177147, 177608, 180000, 181202, 184832, 186050, 187272, 188498, 189728, 190962, 192000, 194688, 195938, 197192, 199712, 202500, 203522, 204800, 206763, 208658, 211250, 212552, 215168, 216482, 223112, 224450, 228488, 229376, 231200, 232562, 235298, 236672, 238050, 238521, 239432, 242208, 243602, 245000, 246402, 247808, 249218, 252050, 253472, 254898, 256328, 262088, 262144, 263538, 264992, 270848, 273800, 278258, 279936, 281250, 285768, 287282, 288800, 293378, 295245, 296450, 297992, 301088, 302642, 307328, 308898, 310472, 312050, 320000.

Some larger examples :