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centered nonagonal n.  and  happy n.

First numbers that belong to both sets:

1, 10, 28, 91, 190, 496, 820, 946, 2080, 2485, 8128, 9730, 11476, 12880, 13366, 16471, 17578, 21115, 25651, 29890, 33670, 35245, 36046, 43660, 46360, 48205, 53956, 56953, 62128, 66430, 69751, 77815, 79003, 80200, 82621, 87571, 90100, 93961, 103285, 107416, 110215, 117370, 123256, 126253, 129286, 133903, 146611, 156520, 158203, 163306, 165025, 177310, 179101, 197506, 226801, 228826, 245350, 249571, 260281, 280126, 303031, 336610, 356590, 392941, 395605, 400960, 409060, 425503, 506521, 515620, 518671, 524800, 530965, 540280, 568711, 621055, 672220, 686206, 700336, 714610, 776881, 799480, 803278, 818560, 822403, 833986, 869221, 873181, 877150, 893116, 925480, 929566, 946000, 954271, 958420, 975106, 983503, 1013176, 1026028, 1030330, 1034641, 1038961, 1060696, 1087075, 1131760, 1149886, 1186570, 1223830, 1280800, 1309771, 1388611, 1459486, 1500778, 1547920, 1579753, 1595791, 1617301, 1738180, 1771903, 1800253, 1869211, 1875016, 1981045, 1993006, 2011015, 2096128, 2158003, 2183005, 2362051, 2407915, 2487565, 2534626, 2588950, 2678455, 2790703, 2797795, 2812006, 2833390, 2862028, 2869210, 2912491, 2956096, 2970703, 3014740, 3029491, 3126250, 3194128, 3278080, 3316600, 3339820, 3488761, 3689686, 3706003, 3779875, 3812941, 3821230, 3896236, 3913003, 3946645, 4014361, 4160170, 4194856, 4203550, 4549636, 4576825, 4631446, 4787965, 4918816, 5060971, 5070520, 5108806, 5128003, 5351356, 5469778, 5489641, 5629690, 5649841, 5781700, 5894461, 5977153, 6018715, 6029128, 6039550, 6123250, 6550390, 7240915, 7263766, 7332535, 7529140, 7540786, 7575778, 7587460, 7599151, 7610851, 7751953, 7799275, 7834861, 7942105, 8002000, 8026021, 8062120, 8110378, 8317081, 8353828, 8402950, 8427565, 8576011, 8813701, 8902090, 9016381, 9131401, 9157060, 9247150, 9298828, 9311770, 9350650, 9363628, 9441685, 9691003, 9704215, 9757153, 9836830, 9850141, 9956953.