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centered pentagonal n.  and  lucky n.

First numbers that belong to both sets:

1, 31, 51, 141, 331, 391, 601, 1501, 2031, 4951, 5641, 6631, 6891, 7701, 9151, 11391, 11731, 12781, 13141, 17431, 17851, 19581, 26781, 27301, 28891, 31081, 31641, 35701, 38131, 38751, 41281, 43231, 43891, 55131, 74391, 77001, 81451, 100501, 103531, 104551, 116101, 133981, 138651, 143401, 149451, 153141, 154381, 158131, 163201, 168351, 184281, 196701, 218301, 219781, 225751, 230281, 237931, 242581, 261631, 288151, 294981, 315951, 323101, 339481, 345031, 367681, 369601, 385141, 391051, 401001, 500641, 509631, 548731, 594141, 643891, 656641, 677301, 708891, 730351, 793831, 796651, 842451, 851181, 862891, 947101, 950181, 962551, 1035231, 1181641, 1195431, 1198891, 1237281, 1240801, 1251391, 1269141, 1337731, 1356081, 1367151, 1457331, 1491891, 1522951, 1534681, 1586031, 1630141, 1662601, 1683051, 1699501, 1782951, 1799881, 1829701, 1833981, 1864081, 1955851, 2022751, 2045301, 2192581, 2206651, 2263381, 2268141, 2287231, 2301601, 2364391, 2418181, 2482531, 2598451, 2603551, 2618881, 2639391, 2665141, 2685831, 2722231, 2848891, 2940351, 3000301, 3022251, 3027751, 3178141, 3183781, 3200731, 3206391, 3223401, 3291891, 3343731, 3361101, 3407641, 3454501, 3525391, 3531331, 3573051, 3579031, 3693601, 3717951, 3773031, 3896881, 4247781, 4326351, 4332931, 4352701, 4405641, 4432231, 4546131, 4566381, 4620601, 4702531, 4764451, 4812891, 4819831, 5037451, 5044551, 5122981, 5130141, 5296201, 5354581, 5361901, 5568891, 5628751, 5711581, 5779801, 5810251, 5840781, 5925151, 5994631, 6181891, 6205501, 6213381, 6244951, 6404001, 6565051, 6597501, 6630031, 6785641, 6818631, 6884851, 6993141, 7127581, 7161391, 7297431, 7365931, 7469281, 7608201, 7634391, 7643131, 7783651, 8095501, 8140551, 8167641, 8203831, 8385981, 8395141, 8505451, 8765641, 8840701, 8878351, 9067801, 9105931, 9134581, 9259251, 9297781, 9365401, 9452701, 9481891, 9569731, 9599101, 9677641, 9726891.