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aban n.  and  centered octagonal n.

First numbers that belong to both sets:

1, 9, 25, 49, 81, 121, 169, 225, 289, 361, 441, 529, 625, 729, 841, 961, 15000129, 19000881, 24000201, 34000561, 39000025, 77000625, 126000625, 251000649, 351000225, 392000401, 399000625, 401000625, 414000409, 659000241, 704000089, 828000625, 975000625, 976000081, 977000049, 978000529, 1044000721, 1061000329, 1097000641, 1268000881, 1283000761, 1375000561, 1598000625, 1602000625, 1900000921, 1928000281, 1988000569, 1998000601, 2263000041, 2379000625, 2406000601, 2417000569, 2606000401, 2624000625, 2878000609, 2928000321, 2966000521, 3240000241, 3356000761, 3597000625, 3603000625, 3761000929, 3808000681, 3830000769, 4040000721, 4282000969, 4730000625, 4814000689, 4880000449, 5073000625, 5131000161, 5388000409, 6336000801, 6396000625, 6404000625, 6604000225, 7320000249, 7881000625, 8247000969, 8322000625, 8784000729, 8787000121, 8790000025, 8793000441, 8938000681, 9995000625, 9997000225, 9999000025, 10001000025, 10003000225, 10005000625, 10127000689, 10361000521, 10443000481, 11288000025, 11832000625, 12371000625, 12424000369, 13586000481, 13700000209, 14098000225, 14394000625, 14406000625, 14468000089, 15296000329, 16079000809, 16583000625, 17220000625, 18862000921, 18950000281, 19363000801, 19593000625, 19607000625, 20367000369, 21644000161, 21992000209, 22134000625, 22405000489, 22869000625, 24405000841, 24410000169, 24415000009, 24420000361, 24606000769, 24782000929, 25592000625, 25608000625, 25969000201, 27106000321, 27259000609, 27335000889, 28485000625, 29318000625, 29427000849, 29616000649, 32151000249, 32391000625, 32409000625, 32857000225, 35636000625, 36567000625, 37541000025, 37662000489, 39990000625, 39994000225, 39998000025, 40002000025, 40006000225, 40010000625, 41125000849, 41543000041, 42537000025, 43587000625, 44616000625, 44687000449, 47066000809, 47838000961, 47845000225, 47852000001, 47859000289, 48389000625, 48411000625, 49561000129, 52338000625, 53465000625, 57588000625, 57612000625, 58041000889, 61568000641, 61889000625, 63114000625, 63439000641, 67124000889, 67587000625, 67613000625, 72240000625, 73563000625, 76938000129, 78386000625, 78414000625, 79092000289, 79101000001, 79110000225, 79119000961, 80119000809, 83294000449, 83391000625, 84812000625, 86292000025, 87722000041, 88332000849, 89985000625, 89991000225, 89997000025, 90003000025, 90009000225, 90015000625, 93595000489, 93786000025, 95342000625, 96861000625, 101592000225, 102384000625, 102416000625, 102844000249, 107523000649, 107884000849, 108093000625, 109710000625, 112002000889, 112156000609, 112467000321, 114820000201, 115583000625, 115617000625, 117359000929, 117743000769, 118151000361, 118162000009, 118173000169, 118184000841, 121644000625, 122722000489, 123359000625, 123695000209, 124525000161, 127654000369, 129582000625, 129618000625, 130212000801, 131291000281, 131523000921, 135995000625, 137808000625, 139276000809, 141619000329, 144185000089, 144381000625, 144419000625, 145363000225, 146653000209, 147027000481, 150961000369, 151146000625, 153057000625, 155043000025, 158252000481, 158572000521, 159494000689, 159980000625, 159988000225, 159996000025, 160004000025, 160012000225, 160020000625, 164397000681, 165022000441, 165035000025, 165048000121, 165061000729, 167097000625, 167434000969, 169106000625, 171763000249, 175339000225, 176379000625, 176421000625, 176737000801, 181985000409, 183500000161, 183848000625, 185023000449, 185431000689, 185955000625, 188845000969, 190479000721, 191943000769, 192099000681, 192434000929, 193578000625.

Some larger examples :