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centered square n.  and  Curzon n.

First numbers that belong to both sets:

1, 5, 41, 113, 221, 545, 761, 1013, 1625, 3281, 4901, 5513, 6161, 6845, 7565, 10805, 14621, 23981, 25313, 28085, 29525, 31001, 32513, 37265, 44105, 45905, 47741, 51521, 59513, 61601, 65885, 68081, 70313, 74885, 86945, 89465, 92021, 97241, 99905, 102605, 113765, 125501, 131585, 150701, 154013, 157361, 164165, 181805, 185441, 211901, 227813, 231881, 244301, 252761, 283505, 301865, 325625, 335381, 350285, 375845, 391613, 402305, 407705, 413141, 435245, 457925, 469481, 481181, 511061, 535613, 573521, 619385, 639581, 653225, 695021, 730841, 738113, 745421, 760145, 767561, 775013, 859361, 883121, 939821, 1015313, 1032485, 1120505, 1138541, 1184261, 1221485, 1278401, 1297661, 1307345, 1317065, 1336613, 1386113, 1406165, 1416245, 1508585, 1529501, 1625405, 1668965, 1690961, 1746581, 1814513, 1872113, 1883741, 1907105, 1942421, 1990013, 2038181, 2050313, 2111513, 2161121, 2173613, 2274845, 2287661, 2391485, 2404625, 2431013, 2444261, 2470865, 2497613, 2551541, 2606045, 2619761, 2647301, 2773013, 2887205, 2901641, 2959745, 3003701, 3092585, 3107525, 3213113, 3289613, 3335945, 3351461, 3461081, 3508601, 3540461, 3636905, 3685613, 3701921, 3767513, 3800525, 3900425, 3934013, 3967745, 3984665, 4069805, 4330625, 4348301, 4366013, 4473041, 4509005, 4654301, 4746281, 4783325, 4839161, 4989641, 5046665, 5065745, 5104013, 5123201, 5161685, 5278001, 5317061, 5375921, 5395613, 5474741, 5514521, 5594513, 5735885, 5940905, 5961605, 6170585, 6297701, 6319013, 6447641, 6490805, 6534113, 6555821, 6664901, 6686825, 6708785, 6796985, 6930365, 7132865, 7178261, 7201013, 7246625, 7292381, 7453661, 7500065, 7523321, 7663613, 7876481, 7948085, 8483081, 8532581, 8557385, 8732021, 8782241, 8883113, 9010013, 9086585, 9266513, 9422141, 9448205, 9526613, 9710825, 9870125, 9923513, 10138505, 10246865, 10301261, 10328513, 10465313, 10575401, 10713821, 10769441, 10825205, 11021513, 11049701, 11191181, 11333561, 11419421, 11505605, 11563241, 11824385, 12000101, 12088445, 12206741, 12295841, 12385265, 12475013, 12505001, 12655481, 12685685, 12715925, 12776513, 12959141, 13050941, 13112321, 13328285, 13514801, 13546013, 13639865, 13797005, 13891721, 14050301, 14177813, 14338013, 14402345, 14499113, 14596205, 14726165, 14889425, 15086525, 15119501, 15284921, 15417905, 15451241, 15618461, 15685601, 15786581, 16296341, 16364921, 16399265, 16433645, 16640681, 16675313, 16709981, 16779425, 16814201, 16953665, 17023613, 17093705, 17128805.

Some larger examples :