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pancake n.  and  self n.

First numbers that belong to both sets:

1, 7, 121, 154, 211, 277, 1177, 1379, 2279, 2347, 6217, 6329, 8002, 8129, 8386, 8779, 12247, 13696, 17206, 19702, 25879, 26566, 27029, 30629, 35779, 38782, 46972, 48829, 54286, 55612, 58312, 58997, 62129, 62836, 74692, 76246, 84256, 85492, 97021, 97462, 111157, 111629, 135982, 138076, 142846, 153736, 155962, 162736, 172579, 174346, 176122, 197507, 199397, 212227, 224116, 228827, 237017, 255256, 263176, 272692, 278632, 281626, 294529, 299152, 310079, 334972, 358282, 360826, 363379, 366797, 379757, 381502, 392056, 418156, 419987, 421822, 429202, 451726, 454582, 476777, 481672, 488567, 492529, 499501, 526852, 549677, 550726, 552827, 554932, 563392, 565517, 617717, 635629, 642412, 668747, 669904, 674542, 681529, 682697, 686207, 689726, 694432, 695611, 711029, 731446, 735079, 738721, 739937, 749701, 754607, 758297, 760762, 770662, 794431, 800746, 812176, 814727, 817282, 827542, 833987, 849557, 860017, 862642, 867904, 893117, 898471, 909227, 914629, 922762, 929567, 961192, 973711, 975107, 986311, 987716, 991937, 996167, 1003237, 1026029, 1044736, 1063612, 1075312, 1081186, 1110796, 1149887, 1157482, 1166629, 1174279, 1183492, 1205129, 1226962, 1231666, 1236379, 1263256, 1282402, 1285607, 1300079, 1303306, 1355482, 1358777, 1362076, 1363727, 1383617, 1390279, 1447552, 1459487, 1464617, 1466329, 1485227, 1530376, 1535629, 1556731, 1563797, 1569107, 1572652, 1610116, 1649837, 1653472, 1668052, 1671707, 1677197, 1684531, 1699247, 1706629, 1712176, 1717732, 1760627, 1781329, 1783217, 1848004, 1849927, 1900276, 1908082, 1923742, 1927667, 1959211, 2055379, 2061466, 2067562, 2124892, 2137279, 2147629, 2218672, 2239787, 2297297, 2301586, 2320936, 2364226, 2368577, 2372932, 2390392, 2394767, 2427707, 2429911, 2436529, 2443156, 2509921, 2525629, 2527877, 2534627, 2550412, 2561717, 2636957, 2664587, 2671517, 2676142, 2736631, 2738971, 2776547, 2781262, 2797796, 2804897, 2812007, 2842921, 2850079, 2859637, 2874004, 2919737, 2929411, 2931832, 2956097, 2973142, 2975581, 2982904, 2985347, 3041812, 3056629, 3066527, 3096317, 3108772, 3128752, 3161356, 3211846, 3216917, 3221992, 3247427, 3252526, 3285767, 3288331, 3303736, 3370907, 3409967, 3412579, 3428272, 3501982, 3528497, 3549781, 3568457, 3630166, 3763397, 3779876, 3837836, 3854477, 3865591, 3873937, 3879506, 3896237, 3918601, 3927004, 4056977.

Some larger examples :