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centered pentagonal n.  and  happy n.

First numbers that belong to both sets:

1, 31, 226, 331, 391, 3331, 3706, 3901, 6376, 6631, 13141, 15801, 16606, 19141, 20026, 21856, 23281, 25756, 33931, 41281, 42576, 50056, 63601, 66016, 75256, 85101, 97516, 99501, 104551, 106606, 107641, 136306, 144601, 147016, 170956, 172266, 176226, 180231, 181576, 182926, 191131, 193906, 208081, 215356, 218301, 228766, 230281, 231801, 245706, 252016, 256801, 263251, 281401, 289851, 328516, 332151, 333976, 389076, 393031, 411076, 454756, 461176, 496176, 505126, 572406, 582016, 591706, 636301, 722266, 738481, 754876, 828001, 833766, 871726, 874681, 907516, 940956, 965656, 968766, 1000141, 1035231, 1041676, 1061131, 1147516, 1198891, 1202356, 1230256, 1240801, 1244326, 1480326, 1554331, 1606006, 1622076, 1716031, 1855456, 1903141, 1907506, 1929406, 1964706, 1973581, 1995856, 2058891, 2077081, 2090776, 2122906, 2164576, 2220766, 2292016, 2320831, 2388766, 2447776, 2497501, 2507506, 2527576, 2552776, 2603551, 2634256, 2685831, 2758876, 2795766, 2801056, 2806351, 2886376, 2962081, 3000301, 3038766, 3077476, 3144406, 3212056, 3251851, 3280426, 3378516, 3513526, 3519456, 3543226, 3730156, 3809976, 3822331, 3828516, 3865731, 3871951, 3896881, 3978456, 3984766, 4176391, 4195801, 4221751, 4326351, 4332931, 4365906, 4458901, 4552876, 4586676, 4661476, 4681981, 4716256, 4736881, 4757551, 4819831, 4854606, 4938576, 4987891, 5080126, 5087256, 5137306, 5187601, 5202016, 5332651, 5391231, 5546526, 5688931, 5704026, 5734276, 5787406, 5802631, 5840781, 5863731, 5871391, 5879056, 5894401, 5940556, 5948266, 5955981, 6041176, 6205501, 6324226, 6340141, 6428031, 6589381, 6613756, 6630031, 6851701, 6909766, 6943056, 6968076, 7127581, 7254781, 7357351, 7391701, 7452006, 7564651, 7573351, 7582056, 7686906, 7898766, 7970026, 8032641, 8158606, 8167641, 8212891, 8240101, 8285551, 8294656, 8303766, 8322001, 8376826, 8459401, 8487016, 8523906, 8579391, 8644351, 8690901, 8709556, 8850106, 8868931, 8925526, 8944431, 8972826, 9010756, 9039256, 9058281, 9182431, 9297781, 9336391, 9346056, 9384766, 9442981, 9452701, 9462426, 9520881, 9559951, 9608901, 9667806, 9717031, 9776266, 9835681, 9875391.