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pancake n.  and  pernicious n.

First numbers that belong to both sets:

7, 11, 22, 37, 56, 67, 79, 121, 137, 191, 211, 254, 301, 352, 379, 436, 466, 529, 631, 704, 781, 862, 947, 1036, 1082, 1129, 1177, 1226, 1276, 1327, 1432, 1486, 1597, 1654, 1712, 1831, 2017, 2081, 2279, 2416, 2486, 2629, 3656, 4279, 4657, 4754, 4852, 5152, 5254, 5461, 5672, 5779, 5887, 6217, 6329, 6556, 6671, 7876, 8002, 8257, 8647, 8912, 9046, 9592, 9731, 10012, 10586, 11027, 11176, 12247, 12562, 12721, 13204, 13696, 13862, 14366, 15401, 16654, 17206, 17392, 17579, 17956, 18146, 18337, 18529, 18722, 18916, 19504, 20101, 20707, 21322, 22156, 22367, 22579, 22792, 25201, 25426, 26107, 26336, 27967, 28681, 29647, 31376, 32897, 33671, 34192, 34454, 35512, 36857, 37129, 37676, 38504, 38782, 39061, 40187, 41042, 41329, 42196, 42487, 45452, 46972, 49142, 49456, 50404, 52004, 53302, 54286, 55279, 56281, 56954, 57292, 59341, 60727, 62482, 64621, 65342, 66067, 66796, 67162, 67897, 68266, 69379, 73921, 74306, 74692, 75856, 77816, 78211, 79801, 81811, 82216, 83029, 84256, 86321, 87572, 90101, 90952, 91807, 92236, 92666, 94831, 96142, 97021, 97462, 99236, 99682, 100129, 100577, 101026, 101476, 102832, 106031, 106492, 108812, 112102, 113051, 113527, 114482, 117371, 117856, 119806, 121279, 121772, 122266, 122761, 126254, 126757, 128779, 131329, 132871, 133904, 134422, 136504, 139129, 144454, 144992, 147697, 148786, 150976, 151526, 152077, 158204, 159896, 162166, 163307, 169072, 170237, 171992, 172579, 174346, 176122, 177311, 179701, 180301, 181504, 182107, 182711, 183316, 186967, 190654, 191891, 193754, 194377, 196879, 197507, 200662, 203842, 206404, 209629, 210926, 212879, 213532, 216812, 219454, 221446, 222779, 223447, 224116, 228151, 234271, 237706, 239087, 242557, 243254, 244651, 245351, 246052, 249572, 250279, 250987, 252406, 253117, 255971, 256687, 257404, 258841, 259561, 263176, 265357, 270481, 271954, 272692, 274912, 276397, 278632, 280876, 281626, 284636, 285391, 286904, 292996, 295297, 296066, 296836, 299152, 303032, 304591, 306154, 307721, 310079.

Some larger examples :