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balanced prime  and  centered decagonal n.

First numbers that belong to both sets:

211, 20161, 135301, 183361, 286801, 566161, 1193161, 2076901, 2595601, 3702301, 5729851, 6011561, 6322501, 6664351, 8495561, 9405061, 10332031, 13390661, 15868711, 19217801, 19611901, 20210551, 20412101, 21063781, 24608711, 31062781, 35577781, 37387451, 38433781, 41026801, 45677531, 46010611, 54334561, 56464801, 63670961, 73593661, 79900031, 80420551, 81628201, 82722781, 88011101, 91185851, 122735351, 124875031, 136372531, 143835661, 150234211, 157108151, 170382031, 170907811, 176923261, 194906461, 201136531, 210178861, 212323861, 222611281, 225691211, 241408261, 272728051, 280163551, 284371111, 297644701, 350410061, 373204801, 375281161, 392630911, 394494031, 464889031, 475458761, 489802531, 503857411, 532047701, 555616111, 610788781, 641561281, 649059211, 682404031, 683105161, 711207011, 725831761, 736837301, 762427261, 778315261, 836118461, 844285151, 855889861, 877613761, 910102861, 917131961, 919164611, 923372551, 971130161, 1032556351, 1062809101, 1066019011, 1138314161, 1205050501, 1217190031, 1242912611, 1283282101, 1311795031, 1346194361, 1376555281, 1420707961, 1469497961, 1479286001, 1518588781, 1555054301, 1568663281, 1608231451, 1634160811, 1638683561, 1648474031, 1719121531, 1759594201, 1785199601, 1792765801, 1852716251, 1881509011, 1886361761, 1932676301, 1962279551, 2002700911, 2038281451, 2040301001, 2050413751, 2071731901, 2084984101, 2116756001, 2153746351, 2161640281, 2169756961, 2187290701, 2191894531, 2277724961, 2292047551, 2306415031, 2358031861, 2389625911, 2392468751, 2394875551, 2454995611, 2477204111, 2589746611, 2598402061, 2636152411, 2649256711, 2733472711, 2810939051, 2882040361, 2969850061, 3069622531, 3075572011, 3168525511, 3333749311, 3363250801, 3397051451, 3631377751, 3652428781, 3682762301, 3692810761, 3713493781, 3755307151, 3777538411, 3906990811, 4003176601, 4035214361, 4085654051, 4106548111, 4153970761, 4225179151, 4235068561, 4325181661, 4371480961, 4385389201, 4443031451, 4487259031, 4519671451, 4546167811, 4619432101, 4704931501, 4717824031, 4749207901, 4894538281, 5020488281, 5033805851, 5069087201, 5219518951, 5357082781, 5366907031, 5434939651, 5520666061, 5551611811, 5651690101, 5723528611, 5792416661, 5815584601, 5850423211, 5871650461, 5906312651, 5906656351, 5928673951, 6079410151, 6224979701, 6235216411, 6262083551, 6415541101, 6434898751, 6440281051, 6603523111, 6609702611, 6673483111, 6697983001, 6817832011, 6865920961, 7036313411, 7054331411, 7169737781, 7277684761, 7354954811, 7399896851, 7605975031, 7791575501, 7837434361, 7856053411, 7864776301, 7878266651, 7912440901, 8018610811, 8043859951, 8110982261, 8235102361, 8255406611, 8287945411, 8358938281, 8531960861, 8584088951, 8591548781, 8766531281, 8792930801, 8850055561, 8873631281, 8923833811, 8929326701, 8950045861, 9095325751, 9123496861, 9162410281, 9287403511, 9581472001, 9595047211, 9661748611, 9692103781, 9897022951.