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centered square n.  and  de Polignac n.

First numbers that belong to both sets:

1, 1985, 6161, 7813, 9941, 10513, 13285, 17113, 17861, 20201, 35645, 39481, 61601, 66613, 76441, 93745, 106261, 112813, 204161, 211901, 215825, 221113, 223781, 234613, 267181, 277513, 317605, 348613, 353641, 382813, 386321, 389845, 407705, 413141, 440861, 469481, 521221, 546013, 588613, 646385, 767561, 787513, 795061, 800113, 838513, 1029613, 1049801, 1147613, 1159765, 1184261, 1202801, 1209013, 1230881, 1240313, 1268825, 1272013, 1294441, 1320313, 1369513, 1396121, 1399465, 1453513, 1550561, 1582421, 1607425, 1698325, 1705705, 1720513, 1852813, 1891513, 1954265, 1970113, 1978061, 1990013, 2086925, 2115625, 2194513, 2249321, 2287661, 2313401, 2352281, 2444261, 2484221, 2493145, 2551541, 2628925, 2656513, 2735461, 2791885, 2848885, 2901641, 2911285, 2969485, 3018425, 3047981, 3077681, 3087613, 3122501, 3147541, 3197921, 3223261, 3228341, 3335945, 3351461, 3393013, 3461081, 3471613, 3508601, 3577813, 3620741, 3631513, 3822613, 3878113, 4184725, 4236961, 4260281, 4277813, 4324741, 4360105, 4395613, 4473041, 4527041, 4581365, 4678741, 4703245, 4789513, 4801901, 4851613, 4870321, 4876565, 4977013, 5072113, 5084861, 5362813, 5389045, 5408761, 5435105, 5514521, 5527813, 5561113, 5601205, 5628013, 5688565, 5715581, 5729113, 5865313, 5934013, 6030865, 6072613, 6128501, 6226921, 6233981, 6297701, 6354613, 6404621, 6621161, 6841301, 6900613, 6908045, 7239013, 7254241, 7507813, 7624513, 7632325, 7687121, 7757861, 8068145, 8076181, 8116421, 8156761, 8286521, 8294665, 8343613, 8400901, 8425513, 8715313, 8732021, 8883113, 8933765, 8942221, 9112181, 9240701, 9309613, 9318245, 9396113, 9422141, 9474305, 9631661, 9658013, 9684401, 9781465, 9799165, 9816881, 9852361, 9896801, 9905701, 9968113, 10003865, 10093525, 10165541, 10219721, 10575401, 10649113, 10769441, 10788013, 10815901, 10871785, 10909121, 11030905, 11040301, 11106185, 11229061, 11333561, 11400313, 11409865, 11419421, 11659621, 11669281, 11766101, 11873065, 11902321, 11931613, 12276013, 12295841, 12315685, 12635365, 12675613, 12806861, 13030513, 13071385, 13112321, 13276705, 13421381, 13639865, 13650313, 13671221, 13891721, 14145881, 14305901, 14370161, 14531441, 14628641, 14715313, 14802241, 14824013, 14911261, 14954981, 14987813, 14998765, 15075541, 15097513, 15119501, 15152513, 15174541, 15207613, 15218645, 15518021, 15562621, 15708013, 15764113, 15809065, 15955601, 16284925, 16387813, 16537001, 16883861, 17304845, 17434513, 17683405, 17766761, 17850313, 17934061, 18234761, 18246841, 18416381, 18684385, 18708845, 18721081, 18757813, 18880513.

Some larger examples :