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centered heptagonal n.  and  tau n.

First numbers that belong to both sets:

1, 8, 3928, 8576, 13672, 15016, 31256, 33272, 56008, 91288, 127016, 131048, 177976, 232072, 287288, 326656, 355048, 601336, 610072, 697768, 707176, 748672, 922888, 1103488, 1300216, 1426888, 1573496, 1727272, 1903672, 2603672, 2819272, 3235688, 3323776, 3433816, 3454648, 4033408, 5188072, 5464376, 6010936, 6038488, 6336296, 6923848, 7272728, 7568296, 7733888, 7901272, 7932856, 8621656, 8798336, 8943208, 9339128, 9673672, 9708616, 11258248, 12076072, 13315576, 13356568, 13979008, 15398272, 17040248, 17538088, 18043096, 18555272, 19601128, 19650856, 20185208, 20675656, 22059136, 22910728, 23833216, 25865848, 25922968, 26536168, 27784072, 28418776, 29648536, 30966776, 31974272, 32997896, 33689272, 34103168, 34387816, 35873608, 39478328, 40997272, 43724416, 44995336, 45726136, 45802072, 46208128, 47359768, 47437048, 49100696, 49863976, 49943272, 54263672, 55958008, 56857256, 57309568, 57849016, 60148096, 60525928, 60613288, 62403272, 62491976, 65273048, 65363768, 66243976, 70199368, 72220072, 72729728, 74366216, 75923072, 77397272, 78454216, 80690408, 81668056, 81769528, 84946408, 85049896, 86157688, 87272648, 89984896, 90553688, 90660536, 91696648, 92954968, 93533056, 94004072, 94112936, 95168536, 95278072, 97518968, 101098376, 104857208, 108450728, 109075072, 109701208, 112978048, 117354616, 117476248, 119308288, 121278088, 122600248, 125266072, 125391736, 127960568, 129318568, 129446248, 130000256, 133565272, 134258048, 143292808, 143427208, 144864728, 149083208, 149220296, 150686488, 152760448, 156482488, 156622936, 161008072, 161150536, 164204776, 165598168, 167287688, 173391688, 176559272, 176708456, 177355648, 181515608, 182323072, 191168216, 194650072, 203785856, 209108096, 209974696, 211713272, 213459016, 215211928, 216806696, 218739256, 220347016, 225711256, 229493272, 231310696, 232051072, 233135288, 237728128, 238478696, 240331288, 247813336, 249701768, 253678888, 259432216, 262151296, 268183168, 273107528, 274903672, 278888408, 288975688, 294086528, 299242168, 299436376, 300473216, 301316968, 303594488, 305488072, 305684296, 309687848, 316240856, 320513656, 326773672, 327856768, 333299128, 334598272, 346752568, 348776072, 355728248, 357777736, 357990088, 360046072, 360259096, 363462016, 364604248, 367109128, 369191096, 370558336, 371495272, 371711656, 376342856, 378450808, 378669208, 383343416, 385470856, 392777848, 400902272, 402101848, 402326968, 404506376, 408353408, 409336936, 414196168, 416865688, 421538776, 428945896, 434153672, 438922408, 440177536, 446717272, 447983488, 451792888, 459219496, 462030136, 464607368, 472138136, 472382072, 477601048, 481287808, 489448576, 501189928, 506565256, 506817928, 509263672, 511969256, 514682008, 517657288, 524233088, 531367768, 534131368, 536902136, 542203768, 544995368, 547794136, 550863496, 556498216, 565004056, 567853672, 569013376, 570710456.

Some larger examples :