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congruent n.  and  nonagonal n.

First numbers that belong to both sets:

24, 46, 111, 154, 261, 325, 559, 651, 750, 856, 1350, 1639, 1794, 2125, 2301, 2484, 2871, 3286, 3504, 4446, 4959, 5226, 5500, 5781, 6069, 6364, 6975, 7614, 8976, 9334, 10071, 10836, 11229, 11629, 12871, 13299, 13734, 14176, 14625, 15544, 16014, 16975, 18469, 18981, 20026, 20559, 21646, 22200, 23329, 23904, 24486, 25075, 25671, 27501, 28125, 28756, 30039, 31350, 34750, 35451, 36159, 36874, 37596, 38325, 39061, 39804, 41311, 42846, 45201, 46806, 48439, 49266, 50100, 50941, 51789, 53506, 54375, 56134, 57921, 59736, 60654, 61579, 62511, 65349, 66309, 68250, 69231, 71214, 72216, 73225, 75264, 76294, 78375, 81549, 82621, 83700, 85879, 86979, 88086, 89200, 90321, 93726, 96031, 97194, 98364, 99541, 100725, 101916, 104319, 106750, 111696, 112950, 115479, 118036, 119325, 120621, 123234, 124551, 127206, 132600, 133966, 136719, 140901, 142309, 143724, 146575, 149454, 150904, 156774, 158259, 159751, 164269, 165789, 167316, 170391, 173494, 175056, 181374, 184575, 187804, 189429, 191061, 192700, 195999, 199326, 206064, 207766, 211191, 214644, 216381, 218125, 219876, 223399, 226950, 228736, 232329, 234136, 235950, 239599, 241434, 243276, 245125, 246981, 252591, 254475, 256366, 258264, 264000, 265926, 269799, 275661, 277629, 279604, 283575, 287574, 293625, 297694, 299739, 301791, 305916, 307989, 310069, 312156, 314250, 316351, 318459, 320574, 322696, 331254, 335575, 339924, 342109, 344301, 350919, 355366, 357600, 362089, 364344, 366606, 371151, 378021, 380325, 387279, 389611, 391950, 394296, 401376, 403750, 408519, 415725, 418141, 420564, 422994, 425431, 430326, 440200, 442686, 445179, 447679, 452700, 455221, 457749, 460284, 465375, 467931, 470494, 473064, 480816, 483414, 488631, 493876, 496509, 499149, 507111, 512454, 523224, 525934, 531375, 539589, 542341, 547866, 550639, 556206, 559000, 567424, 570246, 575911, 584461, 587325, 590196, 595959, 601750, 604656, 610489, 616350, 622239, 628156, 631125, 634101, 637084, 643071, 649086, 661200, 664246, 670359, 676500, 679581, 682669, 691975, 698214, 704481, 707625, 710776, 713934, 720271, 723450, 729829, 733029, 742671, 749134.

Some larger examples :