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arithmetic n.  and  pancake n.

First numbers that belong to both sets:

1, 7, 11, 22, 29, 37, 46, 56, 67, 79, 92, 137, 154, 191, 211, 254, 277, 301, 326, 352, 379, 407, 497, 596, 631, 667, 742, 781, 821, 862, 947, 991, 1129, 1177, 1276, 1327, 1379, 1486, 1541, 1597, 1654, 1771, 1831, 1892, 2017, 2081, 2279, 2347, 2486, 2557, 2629, 2702, 2851, 2927, 3082, 3161, 3241, 3322, 3404, 3487, 3571, 3742, 3829, 3917, 4006, 4187, 4279, 4466, 4561, 4657, 4951, 5051, 5152, 5254, 5357, 5461, 5566, 5779, 5996, 6106, 6217, 6329, 6556, 6671, 6787, 6904, 7022, 7141, 7261, 7382, 7627, 7751, 7876, 8129, 8257, 8386, 8516, 8647, 8779, 9046, 9181, 9317, 9454, 9731, 9871, 10297, 10441, 10586, 10879, 11027, 11176, 11326, 11477, 11629, 11782, 12091, 12247, 12404, 12562, 12721, 12881, 13367, 13531, 13862, 14029, 14197, 14366, 14536, 14707, 14879, 15052, 15226, 15401, 15577, 15932, 16111, 16291, 16472, 16654, 16837, 17021, 17206, 17579, 17767, 18146, 18337, 18529, 18722, 19111, 19307, 19702, 19901, 20101, 20302, 20707, 20911, 21116, 21322, 21529, 21737, 22156, 22367, 22579, 22792, 23006, 23221, 23437, 23654, 24091, 24311, 24977, 25201, 25652, 25879, 26107, 26336, 26566, 26797, 27029, 27262, 27496, 27731, 27967, 28204, 28681, 28921, 29162, 29647, 29891, 30136, 30382, 30629, 30877, 31126, 31627, 31879, 32132, 32641, 32897, 33671, 33931, 34454, 34717, 34981, 35246, 35512, 35779, 36047, 36586, 36857, 37129, 37676, 37951, 38227, 38782, 39061, 39341, 39622, 39904, 40187, 40471, 40756, 41329, 41617, 41906, 42196, 42487, 42779, 43366, 43661, 43957, 44254, 44851, 45151, 45452, 46057, 46361, 47279, 47587, 48206, 48517, 48829, 49142, 49771, 50087, 50722, 51041, 51361, 52004, 52327, 52651, 53302, 53629, 53957, 54286, 54947, 55279, 55946, 56281, 56617, 57631, 57971, 58654, 58997, 59341, 59686, 60032, 60727, 61076, 61777, 62129, 62482, 62836, 63191, 63547, 64262, 64621, 64981, 65342, 65704.

Some larger examples :