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pernicious n.  and  star n.

First numbers that belong to both sets:

13, 37, 73, 121, 181, 253, 433, 541, 661, 793, 1261, 1441, 1633, 1837, 2053, 2521, 2773, 3313, 3601, 4537, 4873, 6337, 6733, 7561, 8437, 9361, 9841, 10333, 10837, 11353, 12421, 13537, 14113, 16537, 18481, 19153, 22693, 24193, 24961, 25741, 28153, 32413, 33301, 34201, 36037, 36973, 37921, 44893, 49141, 50233, 55873, 57037, 63037, 65521, 74593, 77293, 87121, 99073, 100621, 105337, 108541, 113437, 116761, 121837, 130537, 132313, 139537, 143221, 168337, 180613, 206461, 208693, 210937, 213193, 222337, 224653, 226981, 229321, 236413, 243613, 255853, 263341, 265861, 268393, 270937, 281233, 297037, 299713, 305101, 313273, 321553, 324337, 335593, 338437, 355753, 367537, 373501, 376501, 379513, 388621, 394753, 397837, 407161, 413437, 419761, 426133, 448813, 468721, 482233, 492493, 499393, 502861, 506341, 509833, 516853, 520381, 523921, 527473, 534613, 541801, 545413, 567337, 578461, 597241, 612481, 620173, 635701, 639613, 651421, 655381, 679393, 687493, 695641, 699733, 703837, 707953, 712081, 737101, 741313, 745537, 749773, 762553, 766837, 771133, 779761, 850513, 855037, 864121, 887041, 891661, 896293, 900937, 910261, 919633, 929053, 933781, 991453, 996337, 1006141, 1025893, 1035841, 1040833, 1050853, 1055881, 1060921, 1096537, 1101673, 1111981, 1122337, 1153693, 1158961, 1196173, 1212301, 1239421, 1244881, 1255837, 1300141, 1305733, 1311337, 1345213, 1356601, 1414261, 1420093, 1455337, 1467181, 1473121, 1497001, 1503001, 1527121, 1551433, 1575937, 1582093, 1600633, 1613053, 1625521, 1631773, 1638037, 1663213, 1669537, 1694953, 1707733, 1714141, 1733437, 1739893, 1759333, 1765837, 1785421, 1798537, 1811701, 1824913, 1831537, 1858153, 1911961, 1918741, 1973413, 1980301, 1994113, 2042833, 2056861, 2070937, 2077993, 2127721, 2142037, 2149213, 2156401, 2163601, 2170813, 2178037, 2207053, 2236261, 2332513, 2347501, 2355013, 2400337, 2415541, 2423161, 2469133, 2476837, 2484553, 2492281, 2500021, 2507773, 2531101, 2538901, 2546713, 2554537, 2578081, 2593837, 2601733, 2609641, 2617561, 2625493, 2641393, 2673337, 2705473, 2713537, 2721613, 2754037, 2778481, 2786653, 2794837, 2803033, 2835937, 2885653, 2910673, 2952613, 2969473, 2986381, 3003337, 3020341, 3037393, 3063061, 3088837, 3097453, 3106081, 3123373, 3201781, 3210553, 3219337, 3263437.

Some larger examples :