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nude n.  and  Smith n.

First numbers that belong to both sets:

4, 22, 636, 648, 666, 728, 1111, 1626, 1935, 1962, 2688, 2888, 3168, 3366, 3864, 4464, 6816, 7119, 7784, 8736, 9396, 9648, 12648, 13662, 14688, 14784, 14832, 15115, 17199, 18872, 22368, 22448, 28784, 31488, 32226, 33315, 33384, 34776, 39492, 41436, 43992, 44928, 48248, 48272, 48432, 49824, 51115, 51315, 61992, 62496, 66636, 77364, 77728, 82416, 82488, 82848, 91296, 92448, 93924, 94464, 96696, 99288, 111755, 112368, 116616, 117488, 118448, 119124, 121888, 123126, 124424, 127848, 128832, 131796, 137676, 139896, 141184, 142824, 144624, 146916, 147728, 148824, 149292, 149364, 149616, 155155, 155355, 161448, 161664, 161832, 161928, 162636, 163236, 163626, 163962, 166848, 177128, 177177, 181368, 181448, 183864, 184368, 184824, 188144, 188616, 192888, 192996, 196362, 196992, 212448, 216126, 216162, 216324, 216864, 217448, 219816, 222384, 222966, 224848, 226626, 228248, 228384, 228448, 229932, 229968, 231666, 236262, 236448, 237636, 239364, 243936, 244288, 244488, 246168, 246648, 247184, 262164, 262236, 262368, 262926, 263664, 264216, 264264, 264288, 264816, 266226, 266316, 267288, 268848, 274848, 277326, 278824, 282864, 286992, 287224, 288224, 288848, 293922, 296622, 298872, 299916, 312126, 319392, 323928, 326166, 326196, 328368, 328464, 332964, 334944, 341688, 342888, 343344, 343728, 348192, 348288, 351555, 361488, 361962, 364164, 364932, 368184, 369324, 372372, 373968, 376488, 377664, 381864, 382896, 384384, 386136, 393264, 396936, 398448, 399132, 413688, 413832, 414264, 414648, 416436, 416916, 419184, 426288, 426648, 428448, 428664, 431496, 432144, 436368, 438624, 438984, 441168, 441488, 442488, 444492, 444888, 447216, 448112, 448448, 448464, 448992, 462288, 463248, 463488, 464292, 464664, 467964, 468384, 468432, 471996, 476364, 481368, 481392, 481896, 484344, 486864, 488424, 489384, 496692, 515515, 577395, 579915, 613488, 613644, 616392, 619488, 621636, 624636, 628368, 628992, 636696, 636816, 636912, 638616, 661392, 662832, 663444, 663984, 666132, 666264, 669168, 679392, 681168, 682464, 684264, 684648, 686112, 686784, 691344, 694944, 696492, 696924, 698112, 699624, 714784, 717717, 736848, 741888, 742896, 767172.

Some larger examples :