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equidigital n.  and  vampire n.

First numbers that belong to both sets:

1435, 110758, 117067, 124483, 133245, 135837, 146137, 156289, 180225, 193945, 253750, 296320, 371893, 384912, 489159, 536539, 567648, 568750, 769792, 829696, 841995, 10124757, 10134985, 10229845, 10237864, 10255000, 10269504, 10291779, 10293966, 10294695, 10349527, 10417167, 10429753, 10511694, 10604277, 10687513, 10716300, 10835370, 11165728, 11364138, 11368026, 11369533, 11391250, 11420923, 11522250, 11525490, 11529216, 11536875, 11557323, 11575435, 11632896, 11697835, 11722657, 11728786, 11790166, 11823997, 11833645, 11844832, 11848000, 11883613, 11976178, 12095568, 12159720, 12213585, 12276544, 12384000, 12387735, 12439129, 12447184, 12451927, 12484057, 12489471, 12505000, 12519846, 12574845, 12608743, 12640860, 12735895, 12778155, 12894547, 12955000, 13042849, 13168575, 13225518, 13269258, 13538245, 13568215, 13580379, 13596871, 13628875, 13652482, 13667584, 13764397, 13918621, 13978575, 14027328, 14145799, 14147995, 14220661, 14256081, 14262250, 14397718, 14430496, 14452879, 14622525, 14642208, 14652900, 14676228, 14736640, 14823463, 15028335, 15204672, 15230965, 15243390, 15286077, 15304302, 15379875, 15435000, 15527700, 15569982, 15622713, 15693426, 15768270, 15788416, 15795000, 15806272, 15862063, 15862635, 15930432, 16093728, 16238848, 16296898, 16330752, 16398144, 16757280, 16776720, 16947328, 17068288, 17204359, 17343697, 17428000, 17482000, 17605350, 17834593, 17840128, 17923437, 18026752, 18208750, 18254160, 18280750, 18453595, 18517351, 18524749, 18647023, 18720153, 19262587, 19544341, 19554277.