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hoax n.  and  pentagonal n.

First numbers that belong to both sets:

22, 2625, 4676, 12650, 22632, 56940, 112477, 145860, 158275, 169176, 207390, 211876, 260625, 268182, 279720, 354051, 367290, 400675, 417912, 461760, 554192, 589380, 600717, 602617, 614080, 717950, 823251, 850137, 907537, 916895, 1047926, 1169092, 1171742, 1255380, 1288530, 1387685, 1469655, 1575425, 1646932, 1669010, 1732900, 1904630, 2028272, 2056276, 2177435, 2320682, 2343125, 2414907, 2620865, 2876645, 3139990, 3179176, 3602975, 3635595, 3777060, 3974762, 4197557, 4303607, 4582382, 5138376, 5494137, 5574812, 5626985, 5720337, 6339676, 6358192, 6382922, 6715126, 6945580, 7101376, 7153692, 7186487, 7989142, 8261440, 8819725, 9216922, 9254142, 9630467, 9676130, 9829120, 10248187, 10540376, 10756187, 11391926, 11708257, 11775405, 11994962, 12173777, 12190876, 12207987, 12726897, 12928676, 13381760, 13760747, 13915651, 14487942, 14534597, 14618765, 14938926, 15090790, 15339207, 15686517, 15696220, 15744780, 16681670, 16721712, 16882360, 17216122, 17297526, 17594225, 17635347, 18049207, 19094152, 19136990, 19960032, 20190507, 20666560, 20945885, 21703722, 22139525, 22243376, 22498257, 23307075, 23890126, 24046022, 24262715, 24528882, 24857526, 25533751, 25968801, 26369777, 26546170, 27091625, 27436955, 27952575, 27991440, 28147170, 28407680, 30076487, 30562037, 30589126, 31654957, 33160855, 33259667, 33344480, 33727475, 34069751, 34198550, 34298895, 34773930, 34918525, 35252232, 35470722, 35558307, 35895050, 36277627, 36528870, 36588112, 37317722, 37572535, 38402870, 38966565, 39058362, 39549770, 39966785, 40292642, 40807376, 41925910, 41973505, 42482865, 42530775, 42834832, 43220452, 44960700, 45141551, 45620080, 46151040, 46567990, 47255847, 47306376, 47390651, 47610117, 47880925, 48629607, 49023275, 49280870, 49298067, 49384097, 49746242, 50648676, 51190525, 51770500, 52922430, 53136480, 53547950, 53583805, 55592572, 55793652, 56546330, 56564751, 56841426, 57545357, 57656900, 58066815, 58085482, 58291017, 58609376, 58797051, 59079126, 59569655, 60613995, 60919507, 61436800, 61628945, 61917725, 62826940, 63157437, 63449772, 63899330, 63918912, 64448760, 64822927, 64842650, 64862376, 64901837, 65396112, 65495192, 66170925, 66770040, 67251276, 67271365, 69091660, 69193500, 70174980, 70216025, 70895000, 71452955, 71660160, 72054676, 72784251, 73748710, 74465651, 75228545, 75526276, 76230397, 77281937, 77713207, 77756400, 77799605, 78167332, 78666225, 79188501, 80567697, 80677667, 80831751, 80985982, 82358445, 82647682, 83496051, 83899422, 84483785, 84641460, 85613260, 86704612, 87940645, 88354600, 88446722, 89324275, 89741470, 90043382, 90299242, 92076920, 92429825, 95157855, 95564495, 96356330, 97393017, 97489735, 97659107, 98995002, 99923285.