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aban n.  and  pentagonal n.

First numbers that belong to both sets:

1, 5, 12, 22, 35, 51, 70, 92, 117, 145, 176, 210, 247, 287, 330, 376, 425, 477, 532, 590, 651, 715, 782, 852, 925, 1000825, 2000460, 5000501, 23000626, 32000432, 65000542, 89000462, 114000927, 132000051, 135000010, 166000340, 170000651, 228000197, 254000747, 327000455, 367000425, 385000651, 389000172, 465000870, 573000765, 589000876, 807000440, 1065000651, 1067000026, 1093000557, 1192000055, 1202000142, 1341000050, 1396000320, 1455000965, 1522000047, 1538000651, 1572000507, 1579000815, 1771000301, 1842000252, 1852000997, 2183000227, 2194000915, 2369000751, 2500000525, 2697000412, 2728000651, 2938000945, 2988000820, 3010000026, 3031000980, 3056000585, 3113000926, 3297000092, 3459000651, 3540000310, 3650000697, 3666000735, 4183000892, 4754000165, 4954000207, 5066000780, 5159000651, 5347000685, 5538000585, 5742000026, 5755000251, 5832000797, 6148000651, 6210000302, 6296000660, 6401000775, 6615000492, 6804000075, 7303000376, 8056000195, 8078000645, 8358000651, 8492000225, 8506000972, 8532000632, 8556000675, 8952000387, 9155000002, 9197000562, 9417000517, 9599000026, 9605000651, 9688000751, 9767000027, 9823000202, 9956000615, 11721000215, 11764000442, 11814000640, 11940000332, 12278000357, 12325000651, 12371000930, 12422000505, 13830000651, 14226000801, 14619000565, 14836000730, 14905000892, 15286000427, 16714000942, 16746000570, 17060000651, 17068000026, 17460000537, 17941000155, 18385000795, 18823000651, 19483000552, 20054000001, 20071000600, 20518000426, 20685000926, 20949000437, 21528000100, 21886000500, 21915000140, 22563000651, 22682000957, 22788000676, 23361000026, 23735000626, 23837000551, 23918000300, 24280000680, 24513000426, 24584000651, 25532000501, 26320000712, 27229000370, 27248000872, 27382000595, 27826000501, 28211000830, 28508000470, 28694000067, 28834000651, 28911000426, 29620000032, 29655000551, 29769000626, 30191000026, 30850000676, 30943000880, 31113000651, 31280000270, 32098000992, 32541000637, 33192000660, 33407000926, 33620000426, 33691000807, 33904000275, 34220000001, 35873000651, 36171000910, 36219000455, 37079000652, 37951000235, 38025000025, 38068000720, 38398000026, 38410000651, 40250000817, 40279000202, 42021000127, 42406000912, 42461000132, 42811000930, 42984000801, 43016000832, 43166000662, 43429000960, 43680000651, 43845000052, 44054000250, 46475000651, 46559000510, 47543000520, 48256000885, 49840000145, 50565000612, 50753000732, 52062000751, 52255000651, 52269000026, 52491000200, 53696000605, 54114000985, 54381000835, 54461000265, 55308000651, 55515000410, 56596000182, 58149000376, 60269000832, 61598000651, 62869000251, 62912000026, 63539000987, 63623000775, 63759000265, 63858000185, 63884000390, 64909000651, 65917000535, 66770000995, 67097000257, 67250000312, 67858000107, 68388000532, 70720000967, 71709000651, 72656000795, 73335000926, 73840000026, 75278000651, 75733000365, 76831000440, 77243000751, 77275000607, 78097000905, 79039000327, 79916000732, 80699000240, 80949000301, 80972000212, 82410000477, 82588000651, 82657000932, 84657000450, 84821000915, 85412000752, 85888000772, 86397000026, 86415000651, 86518000262, 86567000620, 87671000242, 88639000605, 89159000905, 89454000935, 90194000447, 90751000457, 90844000490, 91161000602, 91403000876, 94235000651, 95107000312, 96636000232, 97127000322, 97253000262, 98320000651.

Some larger examples :