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aban n.  and  centered heptagonal n.

First numbers that belong to both sets:

1, 8, 22, 43, 71, 106, 148, 197, 253, 316, 386, 463, 547, 638, 736, 841, 953, 20000716, 21000176, 23000363, 27000772, 29000168, 52000096, 66000572, 130000256, 187000766, 236000563, 263000123, 343000351, 372000266, 391000156, 393000343, 424000648, 439000801, 468000863, 471000601, 484000441, 589000147, 592000606, 616000078, 764000476, 854000071, 862000798, 880000073, 884000447, 1346000986, 1687000246, 2296000547, 2455000591, 2504000647, 2562000281, 2749000276, 2835000211, 2987000038, 3012000461, 3112000298, 3126000886, 3332000596, 3403000798, 3535000631, 3755000446, 4015000606, 4029000893, 4152000322, 4270000393, 4379000543, 5479000766, 5544000701, 5726000897, 5977000051, 6226000033, 6284000647, 6405000218, 6922000093, 7686000638, 7920000656, 7953000623, 8041000423, 8191000133, 8865000397, 8954000371, 9148000751, 9269000938, 9426000221, 9703000147, 9877000022, 10266000928, 10353000547, 10545000236, 10871000323, 11880000511, 11920000828, 12389000821, 12513000697, 13162000783, 13384000288, 13600000961, 14138000423, 14439000346, 14925000658, 16685000431, 17069000866, 17690000098, 18174000391, 18273000481, 19243000183, 19386000733, 20075000716, 20481000793, 22090000031, 22193000446, 22393000547, 22407000547, 22504000436, 22889000023, 24343000522, 25576000703, 25914000568, 26883000341, 26910000391, 27190000111, 28060000438, 29082000046, 31331000338, 31962000988, 32826000131, 33204000901, 33361000856, 34723000243, 34813000447, 35576000531, 36172000411, 37116000118, 38078000521, 38211000388, 39005000728, 39039000547, 39658000768, 39911000536, 41280000308, 44813000968, 44897000191, 45070000522, 46013000678, 46391000293, 48961000726, 49830000781, 53430000646, 53793000458, 53872000561, 54179000072, 55758000572, 56034000296, 56324000573, 58004000216, 59910000697, 60130000897, 60355000322, 60679000306, 61925000236, 62298000836, 63210000547, 64068000193, 64231000723, 68085000208, 69918000538, 70354000718, 71285000788, 71572000501, 71983000286, 72200000258, 73135000268, 73782000853, 74675000947, 75261000361, 76103000072, 76707000028, 76848000272, 77173000066, 82888000966, 84761000731, 86634000496, 86893000811, 87106000822, 88893000197, 89586000547, 89614000547, 91397000843, 91526000336, 93185000056, 95525000306, 99704000131, 100598000161, 101103000461, 101965000103, 103411000736, 105123000298, 106397000368, 108083000096, 108583000261, 108789000272, 110856000256, 111516000758, 112361000858, 113678000171, 114540000772, 117102000086, 117489000553, 119827000756, 120582000547, 121269000091, 121488000103, 121732000321, 124109000947, 124415000711, 125179000822, 126501000088, 126730000286, 127620000397, 131161000153, 131344000348, 139148000216, 142412000291, 143184000338, 143995000528, 144218000816, 144417000106, 144545000671, 145891000711, 150564000553, 152953000397, 153844000381, 155650000822, 156848000947, 157422000121, 159210000881, 159440000266, 159899000878, 160561000853, 160867000547, 168013000772, 170836000406, 173363000728, 173550000268, 175142000272, 176875000408, 178577000981, 178819000928, 179416000786, 184948000126, 185618000366, 185947000856, 186677000518, 187692000658, 188078000363, 188531000666, 188700000406, 190729000561, 191177000288, 192255000043, 192713000026, 193364000068, 195532000861, 198810000278, 201579000547, 201621000547, 202664000197, 203605000516, 205107000568, 205385000822, 206001000206, 207551000203, 208300000931, 217559000548, 221951000272, 222152000113, 223222000072, 224972000506, 225686000947, 226850000938.

Some larger examples :