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centered pentagonal n.  and  Duffinian n.

First numbers that belong to both sets:

16, 391, 1156, 1501, 2641, 3901, 6631, 7981, 8851, 10081, 13141, 16201, 22801, 23281, 24751, 27301, 28891, 29431, 35701, 36301, 43231, 45901, 49351, 54391, 58141, 60451, 73531, 77881, 80551, 81451, 91681, 95551, 103531, 112891, 117181, 120451, 129391, 144601, 148231, 154381, 158131, 159391, 163201, 173581, 178891, 189751, 191131, 195301, 202351, 208081, 212431, 219781, 237931, 242581, 263251, 268141, 276391, 281401, 283081, 288151, 296701, 301891, 303631, 308881, 339481, 345031, 352501, 361951, 367681, 369601, 391051, 409051, 423331, 439951, 442051, 448381, 465481, 493951, 500641, 518701, 548731, 555781, 577201, 584431, 596581, 606391, 613801, 643891, 656641, 664351, 666931, 687751, 698281, 706231, 719581, 727651, 730351, 738481, 752131, 760381, 771451, 785401, 793831, 805141, 828001, 830881, 854101, 862891, 865831, 889531, 898501, 910531, 925681, 947101, 962551, 971881, 975001, 1000141, 1022401, 1038451, 1048141, 1051381, 1061131, 1077481, 1090651, 1117231, 1140751, 1167931, 1171351, 1181641, 1198891, 1209301, 1223251, 1240801, 1251391, 1254931, 1283431, 1297801, 1308631, 1341391, 1352401, 1370851, 1385701, 1396891, 1415641, 1430731, 1442101, 1472641, 1476481, 1488031, 1507381, 1534681, 1554331, 1566181, 1570141, 1582051, 1602001, 1614031, 1650391, 1662601, 1666681, 1716031, 1749331, 1766101, 1812631, 1816891, 1851151, 1864081, 1868401, 1903141, 1933801, 1955851, 1969141, 1973581, 1986931, 2009281, 2027251, 2063431, 2081641, 2132131, 2136751, 2173891, 2192581, 2206651, 2230201, 2244391, 2249131, 2287231, 2306401, 2320831, 2359531, 2364391, 2423101, 2477551, 2497501, 2522551, 2537641, 2557831, 2598451, 2603551, 2659981, 2665141, 2680651, 2743141, 2832901, 2848891, 2854231, 2870281, 2913301, 2918701, 2934931, 2962081, 2978431, 2983891, 3027751, 3044281, 3066391, 3094141, 3110851, 3116431, 3161251, 3183781, 3200731, 3246151, 3268981, 3297631, 3314881, 3320641, 3366901, 3390151, 3407641, 3436891, 3549181, 3579031, 3603001, 3651181, 3669331, 3675391, 3742381, 3748501, 3816151, 3840901, 3871951, 3890641, 3896881, 3965851, 3991081, 4022731, 4048141, 4067251, 4099201, 4118431, 4124851, 4144141, 4202281, 4254301, 4280431, 4332931, 4352701, 4379131, 4432231, 4458901, 4492351, 4512481, 4519201, 4539391, 4593451, 4654651, 4675141, 4702531, 4764451, 4840681, 4847641, 4868551, 4903501, 4931551, 4952641, 5009101, 5037451, 5094391.

Some larger examples :