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centered square n.  and  junction n.

First numbers that belong to both sets:

113, 313, 925, 1013, 1405, 2113, 2521, 3613, 4513, 8321, 12013, 14621, 15313, 16021, 17113, 18625, 21013, 30013, 32005, 33025, 35113, 42925, 51521, 58825, 63013, 92021, 103513, 104425, 110921, 114721, 121525, 143113, 163021, 175825, 184225, 201613, 206725, 276025, 286525, 288041, 324013, 332113, 337021, 396941, 400513, 411325, 424121, 431521, 457925, 507025, 543925, 628321, 637321, 699745, 711625, 728425, 755221, 772525, 800113, 835925, 899141, 1001113, 1021021, 1044013, 1081921, 1135525, 1190425, 1234021, 1246621, 1268825, 1291225, 1304113, 1320313, 1372825, 1409521, 1456925, 1611013, 1791725, 1818325, 1845121, 1883741, 1918841, 1982041, 2010013, 2058421, 2086925, 2115625, 2132113, 2161121, 2190325, 2219725, 2266321, 2296225, 2322013, 2520013, 2712121, 2744825, 2810821, 2858441, 2863225, 2979241, 3052921, 3072721, 3142525, 3233425, 3269125, 3305021, 3325621, 3361825, 3398225, 3492725, 3669341, 4001621, 4081225, 4086941, 4121321, 4178941, 4266121, 4377841, 4473041, 4521025, 4527041, 4672625, 4783325, 4932941, 5053021, 5213221, 5258525, 5304025, 5421925, 5474741, 5634725, 5749441, 5756225, 5892745, 5982341, 6051721, 6149525, 6276425, 6447641, 6819125, 7005025, 7065041, 7110221, 7185841, 7246625, 7300021, 7330621, 7376641, 7384325, 7445941, 7538845, 7632325, 7964041, 7972025, 8164841, 8237741, 8433725, 8474845, 8582225, 8640325, 8782241, 8891545, 8993041, 9001525, 9069541, 9120721, 9214925, 9283741, 9387445, 9710825, 9825745, 9870125, 9977045, 10030721, 10102513, 10511113, 10547825, 10769441, 11077925, 11143921, 11181721, 11314525, 11400313, 11476841, 11553625, 11621021, 11727325, 11795225, 11970725, 12108121, 12295841, 12715925, 12959141, 13040725, 13112321, 13225225, 13297325, 13411021, 13483625, 13566841, 13734041, 13818025, 13828541, 14007925, 14273825, 14628641, 14944045, 15086525, 15163525, 15240721, 15362425, 15440125, 15495745, 15629641, 15719225, 15921725, 16000825, 16193741, 16205125, 16296341, 16410721, 16491025, 16571525, 16767841, 17058641, 17163941, 17446325, 17946041, 18042025, 18054041, 18246841, 18343625, 18355741, 18562325, 18806845, 19090021, 19263425, 19475041, 19587541, 19738045, 19901741, 20028121, 20524825, 20614621, 20756125, 20859341, 21261721, 21313921, 21667945, 21826225, 21839441, 22064725, 22157825, 22211113, 22251121, 22398125, 22842041, 23167625, 23509225, 23605321, 23742941, 23867141, 24088741, 24102625, 24353221, 24437041, 24563041, 24900625, 24914741, 25056121, 25155325, 25254725, 25439845, 25496941, 25797745, 25855241, 26945141, 27077441, 27431825.

Some larger examples :