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amenable n.  and  pancake n.

First numbers that belong to both sets:

1, 16, 29, 37, 56, 92, 121, 137, 172, 232, 277, 301, 352, 436, 497, 529, 596, 704, 781, 821, 904, 1036, 1129, 1177, 1276, 1432, 1541, 1597, 1712, 1892, 2017, 2081, 2212, 2416, 2557, 2629, 2776, 3004, 3161, 3241, 3404, 3656, 3829, 3917, 4096, 4372, 4561, 4657, 4852, 5152, 5357, 5461, 5672, 5996, 6217, 6329, 6556, 6904, 7141, 7261, 7504, 7876, 8129, 8257, 8516, 8912, 9181, 9317, 9592, 10012, 10297, 10441, 10732, 11176, 11477, 11629, 11936, 12404, 12721, 12881, 13204, 13696, 14029, 14197, 14536, 15052, 15401, 15577, 15932, 16472, 16837, 17021, 17392, 17956, 18337, 18529, 18916, 19504, 19901, 20101, 20504, 21116, 21529, 21737, 22156, 22792, 23221, 23437, 23872, 24532, 24977, 25201, 25652, 26336, 26797, 27029, 27496, 28204, 28681, 28921, 29404, 30136, 30629, 30877, 31376, 32132, 32641, 32897, 33412, 34192, 34717, 34981, 35512, 36316, 36857, 37129, 37676, 38504, 39061, 39341, 39904, 40756, 41329, 41617, 42196, 43072, 43661, 43957, 44552, 45452, 46057, 46361, 46972, 47896, 48517, 48829, 49456, 50404, 51041, 51361, 52004, 52976, 53629, 53957, 54616, 55612, 56281, 56617, 57292, 58312, 58997, 59341, 60032, 61076, 61777, 62129, 62836, 63904, 64621, 64981, 65704, 66796, 67529, 67897, 68636, 69752, 70501, 70877, 71632, 72772, 73537, 73921, 74692, 75856, 76637, 77029, 77816, 79004, 79801, 80201, 81004, 82216, 83029, 83437, 84256, 85492, 86321, 86737, 87572, 88832, 89677, 90101, 90952, 92236, 93097, 93529, 94396, 95704, 96581, 97021, 97904, 99236, 100129, 100577, 101476, 102832, 103741, 104197, 105112, 106492, 107417, 107881, 108812, 110216, 111157, 111629, 112576, 114004, 114961, 115441, 116404, 117856, 118829, 119317, 120296, 121772, 122761, 123257, 124252, 125752, 126757, 127261, 128272, 129796, 130817, 131329, 132356, 133904, 134941, 135461, 136504, 138076, 139129, 139657, 140716, 142312, 143381, 143917, 144992, 146612, 147697, 148241, 149332, 150976, 152077, 152629, 153736, 155404, 156521, 157081.

Some larger examples :