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Duffinian n.  and  star n.

First numbers that belong to both sets:

121, 253, 793, 1261, 1633, 1837, 2773, 3601, 3901, 4213, 4537, 4873, 5221, 7141, 8437, 9361, 9841, 11881, 14113, 14701, 15301, 16537, 17173, 17821, 19153, 19837, 21241, 22693, 23437, 24193, 24961, 26533, 28153, 28981, 29821, 30673, 31537, 34201, 37921, 38881, 39853, 40837, 41833, 43861, 45937, 48061, 50233, 51337, 53581, 55873, 58213, 59401, 63037, 64273, 70633, 73261, 74593, 77293, 78661, 80041, 81433, 84253, 85681, 88573, 90037, 94501, 97537, 99073, 103753, 106933, 115093, 116761, 118441, 120133, 121837, 125281, 127021, 128773, 130537, 134101, 135901, 141373, 143221, 145081, 150733, 154561, 158437, 160393, 162361, 166333, 168337, 172381, 174421, 180613, 184801, 186913, 189037, 193321, 195481, 197653, 199837, 202033, 204241, 208693, 210937, 217741, 224653, 226981, 231673, 234037, 236413, 246037, 250921, 260833, 263341, 268393, 273493, 276061, 278641, 289081, 294373, 297037, 299713, 302401, 310537, 316021, 324337, 332761, 335593, 338437, 361621, 367537, 370513, 382537, 391681, 394753, 397837, 400933, 404041, 407161, 410293, 413437, 419761, 422941, 426133, 429337, 432553, 435781, 442273, 448813, 452101, 458713, 462037, 468721, 472081, 475453, 478837, 485641, 492493, 495937, 499393, 513337, 516853, 523921, 527473, 531037, 534613, 541801, 545413, 552673, 559981, 563653, 567337, 571033, 578461, 582193, 585937, 589693, 593461, 597241, 601033, 620173, 627913, 631801, 635701, 639613, 643537, 651421, 655381, 663337, 671341, 675361, 687493, 691561, 712081, 716221, 732901, 737101, 741313, 745537, 754021, 758281, 762553, 766837, 771133, 784093, 788437, 801541, 810337, 814753, 819181, 828073, 832537, 837013, 841501, 846001, 850513, 855037, 859573, 868681, 873253, 887041, 905593, 910261, 929053, 938521, 948037, 962401, 967213, 972037, 976873, 981721, 996337, 1001233, 1006141, 1011061, 1015993, 1020937, 1025893, 1030861, 1035841, 1045837, 1060921, 1071037, 1081201, 1096537, 1111981, 1122337, 1127533, 1132741, 1137961, 1153693, 1164241, 1174837, 1180153, 1185481, 1196173, 1201537, 1206913, 1217701, 1223113, 1233973, 1244881, 1250353, 1255837, 1277893, 1305733, 1311337, 1328221, 1333873, 1339537, 1345213, 1350901, 1356601, 1362313, 1368037, 1373773, 1379521, 1385281, 1391053.

Some larger examples :