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equidigital n.  and  octagonal n.

First numbers that belong to both sets:

1, 21, 133, 1281, 1408, 1541, 1825, 2133, 3008, 10325, 11041, 12160, 13333, 14981, 15841, 18565, 19521, 23585, 28033, 39445, 46625, 48896, 100101, 102305, 109061, 110208, 111361, 120801, 123221, 125665, 130625, 133141, 136960, 138245, 150080, 154133, 168033, 179585, 188501, 197633, 206981, 219781, 229633, 236321, 246533, 256961, 260485, 282133, 293281, 306560, 328021, 352261, 625633, 1011521, 1022000, 1032533, 1050208, 1053761, 1071616, 1075205, 1082401, 1107776, 1148245, 1163141, 1193221, 1197008, 1227520, 1239061, 1254533, 1258416, 1289696, 1301525, 1309441, 1313408, 1357441, 1373633, 1398101, 1410416, 1506625, 1549445, 1584133, 1592865, 1628033, 1636885, 1690501, 1717633, 1722176, 1735841, 1767936, 1772545, 1791041, 1856533, 1870720, 1904033, 1961825, 2030341, 2050133, 2060065, 2110085, 2120161, 2181121, 2186240, 2201633, 2295125, 2337301, 2353216, 2358533, 2406656, 2466133, 2487941, 2587265, 2722721, 2768641, 2826581, 2891008, 2896901, 2944261, 2980033, 3143680, 3174465, 3280256, 4041441, 4426245, 4595456, 4617761, 4685000, 5619745, 6383125, 6720033, 7889408, 8676801, 9184000, 9469633, 9630208, 10043040, 10098005, 10164161, 10186261, 10252705, 10319365, 10341633, 10386241, 10633301, 10746561, 10757920, 10769285, 10792033, 10837601, 10974881, 10997845, 11020833, 11055360, 11089941, 11136133, 11182421, 11298561, 11310208, 11321861, 11415301, 11427008, 11509125, 11532641, 11674241, 11697925, 11781008, 11816705, 11996000, 12032021, 12056065, 12068096, 12273541, 12297825, 12322133, 12370821, 12541985, 12566533, 12615701, 12887841, 12937633, 13012501, 13314133, 13390081, 13440833, 13542625, 13568133, 13644801, 13657600, 13747361, 13773061, 13785920, 13953633, 14005441, 14161441, 14213633, 14292101, 14397061, 14476033, 14555221, 14608133, 14687681, 14767445, 14794081, 14847425, 14927621, 15008033, 15048320, 15088661, 15115585, 15277633, 15481408, 15604321, 15741461, 15906821, 15920640, 16100833, 16324001, 16520533, 16661633, 16718241, 16817536, 16945633, 17131520, 17174561, 17318421, 17376133, 17709840, 17739008, 17753601, 17812033, 17870561, 18135125, 18194181, 18312581, 18342241, 18550533, 18790021, 18940481, 19000833, 19015936, 19061281, 19212821, 19578965, 19609633, 19855841, 19979521.