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aban n.  and  centered square n.

First numbers that belong to both sets:

1, 5, 13, 25, 41, 61, 85, 113, 145, 181, 221, 265, 313, 365, 421, 481, 545, 613, 685, 761, 841, 925, 12000101, 16000825, 17000281, 63000313, 108000905, 137000905, 196000201, 207000205, 333000625, 336000965, 352000045, 414000313, 487000841, 488000041, 489000265, 522000361, 634000441, 754000945, 799000313, 801000313, 838000861, 861000505, 950000461, 964000141, 994000285, 999000301, 1182000821, 1203000301, 1266000881, 1303000201, 1312000313, 1327000645, 1439000305, 1464000161, 1483000261, 1584000613, 1620000121, 1678000381, 1821000901, 1832000981, 1904000341, 1915000385, 1931000513, 2020000361, 2141000485, 2208000605, 2365000313, 2407000345, 2440000225, 2634000781, 2671000961, 2694000205, 3168000401, 3198000313, 3202000313, 3272000513, 3302000113, 3660000125, 3740000585, 3749000641, 3762000541, 4161000313, 4392000365, 4395000013, 4398000685, 4469000341, 4578000985, 4840000885, 5045000801, 5644000013, 5674000865, 5792000821, 5916000313, 6212000185, 6297000865, 6793000241, 6850000105, 6931000585, 7049000113, 7093000513, 7197000313, 7203000313, 7234000045, 7408000921, 7648000165, 7750000501, 8610000313, 8733000641, 9431000461, 9475000141, 9502000513, 10327000613, 10822000081, 10996000105, 11067000313, 12205000085, 12210000181, 12303000385, 12391000465, 12796000313, 12804000313, 12970000741, 13553000161, 13833000781, 14090000581, 14200000765, 14304000661, 14475000805, 14537000561, 14659000313, 14808000325, 15069000805, 16092000601, 16688000741, 17818000313, 18264000565, 18831000245, 18978000665, 19993000613, 19995000313, 19997000113, 19999000013, 20001000013, 20003000113, 20005000313, 20007000613, 22308000313, 23497000981, 23533000405, 23919000481, 23926000001, 23933000545, 26169000313, 27338000621, 28794000313, 28806000313, 29383000945, 29841000701, 30784000321, 31557000313, 32420000885, 32841000613, 33562000445, 34360000513, 35938000705, 36120000313, 37518000665, 38469000065, 39193000313, 39207000313, 39410000501, 39451000513, 39546000145, 39555000113, 39795000845, 40405000721, 40643000725, 41375000785, 41647000225, 41862000601, 42406000313, 42585000961, 43146000013, 43861000021, 44166000425, 46054000525, 46893000013, 47142000625, 47671000313, 50507000965, 50796000113, 50914000513, 50944000801, 51043000541, 51192000313, 51208000313, 51422000125, 52939000661, 53654000621, 53942000425, 54855000313, 54969000881, 56001000445, 56078000305, 57073000513, 57146000521, 57410000101, 57731000605, 59070000613, 59081000005, 59092000421, 60334000565, 60822000313, 61058000701, 61361000245, 61650000941, 63827000185, 64791000313, 64809000313, 65106000401, 68199000521, 68904000313, 69588000985, 69638000405, 70638000845, 75573000313, 78118000645, 78901000525, 79126000241, 79286000261, 79747000345, 79986000613, 79990000313, 79994000113, 79998000013, 80002000013, 80006000113, 80010000313, 80014000613, 81648000901, 82511000221, 82524000061, 82537000925, 83717000485, 83857000921, 84553000313, 85913000681, 90409000765, 91750000081, 91924000313, 92918000785, 94386000721, 96217000465, 96789000313, 96811000313, 97398000725, 98964000941, 99355000681, 99989000861, 100434000745, 101627000285, 101802000313, 102044000561, 102346000021, 104098000613, 106789000513, 107147000281, 107732000381, 108988000321, 109244000165, 109845000761, 109860000025, 109875000313, 112494000121, 112531000825, 114928000745, 115188000313, 115212000313.

Some larger examples :