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hoax n.  and  nude n.

First numbers that belong to both sets:

22, 336, 424, 735, 1111, 1116, 1344, 1626, 1824, 2166, 2232, 2616, 3339, 3393, 3933, 4116, 4212, 4344, 4824, 8224, 9333, 11124, 11232, 11688, 12144, 12366, 12612, 13848, 14144, 14288, 15115, 18168, 18624, 22144, 22266, 22444, 22488, 22632, 24128, 24216, 24264, 31266, 32226, 33168, 33315, 33336, 33864, 33912, 35955, 36384, 42184, 43224, 43248, 43416, 51115, 51315, 53595, 61128, 61212, 61368, 61848, 63162, 69624, 71575, 79317, 82224, 82248, 84144, 84224, 88224, 98136, 99612, 111168, 111448, 111755, 111924, 112128, 112416, 112728, 113688, 114384, 114648, 114984, 115335, 116664, 117775, 118824, 121662, 121848, 121932, 123126, 123288, 123336, 123696, 126126, 126288, 126324, 126648, 128328, 131424, 131832, 132648, 133326, 133344, 136128, 138312, 139248, 141488, 141864, 142448, 143316, 143496, 144144, 146616, 155155, 155355, 161136, 162162, 162168, 162216, 163344, 163626, 164184, 164232, 164328, 164424, 166224, 167244, 171724, 177177, 181144, 181464, 183216, 184112, 184488, 189432, 191448, 191916, 192366, 194112, 196164, 199224, 211824, 214164, 216216, 216336, 216444, 216648, 218184, 218328, 218616, 219132, 221364, 221436, 221872, 222192, 222336, 223248, 223344, 224424, 226164, 226626, 227444, 228872, 229122, 229626, 231288, 231624, 231666, 233448, 234216, 234396, 236832, 243324, 244164, 248112, 261264, 261384, 261432, 261816, 262224, 262824, 266226, 281224, 281824, 282168, 282336, 283128, 288312, 293364, 296424, 311424, 312126, 312384, 312444, 312636, 312864, 312912, 313368, 316248, 316332, 318336, 319113, 324324, 324432, 326166, 326184, 326322, 328344, 328824, 331368, 331416, 332688, 336612, 337995, 341424, 341448, 343488, 344328, 351555, 362112, 362616, 363336, 364632, 364728, 366384, 366966, 367164, 368424, 371448, 376362, 383832, 384888, 386232, 391626, 392328, 392616, 392922, 395595, 399222, 411288, 413424, 413436, 414412, 414424, 414888, 418632, 422316, 422444, 422688, 424144, 428616, 428832, 432168, 432336, 432432, 433296, 433332, 433824, 436344, 441412, 442124, 442288, 442692, 442824, 442944, 444264, 444636, 461196, 461916, 462312, 462492, 464136, 464232, 468336, 472164, 473172, 474824, 482136, 482144.

Some larger examples :