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pseudoperfect n.  and  upside-down n.

First numbers that belong to both sets:

28, 258, 456, 654, 852, 2288, 2828, 4736, 6464, 8372, 43576, 45556, 81592, 211998, 212898, 213798, 214698, 215598, 216498, 217398, 218298, 219198, 221988, 222888, 223788, 224688, 225588, 226488, 227388, 228288, 229188, 231978, 232878, 233778, 234678, 235578, 236478, 237378, 238278, 239178, 241968, 242868, 243768, 244668, 245568, 246468, 247368, 248268, 249168, 251958, 252858, 253758, 254658, 255558, 256458, 257358, 258258, 259158, 261948, 262848, 263748, 264648, 265548, 266448, 267348, 268248, 269148, 271938, 272838, 273738, 274638, 275538, 276438, 277338, 278238, 279138, 281928, 282828, 283728, 284628, 285528, 286428, 287328, 288228, 289128, 291918, 292818, 293718, 294618, 295518, 296418, 297318, 298218, 299118, 411996, 412896, 413796, 414696, 415596, 416496, 417396, 418296, 419196, 421986, 422886, 423786, 424686, 425586, 426486, 427386, 428286, 429186, 431976, 432876, 433776, 434676, 435576, 436476, 437376, 438276, 439176, 441966, 442866, 443766, 444666, 445566, 446466, 447366, 448266, 449166, 451956, 452856, 453756, 454656, 455556, 456456, 457356, 458256, 459156, 461946, 462846, 463746, 464646, 465546, 466446, 467346, 468246, 469146, 471936, 472836, 473736, 474636, 475536, 476436, 477336, 478236, 479136, 481926, 482826, 483726, 484626, 485526, 486426, 487326, 488226, 489126, 491916, 492816, 493716, 494616, 495516, 496416, 497316, 498216, 499116, 532875, 539175, 555555, 563745, 611994, 612894, 613794, 614694, 615594, 616494, 617394, 618294, 619194, 621984, 622884, 623784, 624684, 625584, 626484, 627384, 628284, 629184, 631974, 632874, 633774, 634674, 635574, 636474, 637374, 638274, 639174, 641964, 642864, 643764, 644664, 645564, 646464, 647364, 648264, 649164, 651954, 652854, 653754, 654654, 655554, 656454, 657354, 658254, 659154, 661944, 662844, 663744, 664644, 665544, 666444, 667344, 668244, 669144, 671934, 672834, 673734, 674634, 675534, 676434, 677334, 678234, 679134, 681924, 682824, 683724, 684624, 685524, 686424, 687324, 688224, 689124, 691914, 692814, 693714, 694614, 695514, 696414, 697314, 698214, 699114, 811992, 812892, 813792, 814692, 815592, 816492, 817392, 818292, 819192, 821982, 822882, 823782, 824682, 825582, 826482, 827382, 828282, 829182, 831972, 832872.

Some larger examples :