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aban n.  and  centered pentagonal n.

First numbers that belong to both sets:

1, 6, 16, 31, 51, 76, 106, 141, 181, 226, 276, 331, 391, 456, 526, 601, 681, 766, 856, 951, 1000141, 2000326, 3000301, 14000806, 15000126, 22000306, 102000391, 219000601, 231000391, 245000251, 440000056, 449000506, 503000101, 604000981, 610000051, 639000391, 641000391, 743000901, 958000501, 1069000906, 1133000581, 1163000481, 1197000106, 1205000176, 1253000391, 1451000931, 1597000876, 1640000391, 1718000026, 1731000706, 1806000016, 1830000201, 1980000766, 2025000151, 2092000641, 2337000126, 2380000426, 2397000651, 2429000176, 2454000576, 2525000451, 2558000391, 2562000391, 2649000381, 2760000756, 3050000281, 3199000531, 3278000776, 3453000151, 3684000391, 3742000081, 3911000641, 3931000156, 3960000501, 4090000641, 4329000391, 4527000906, 4575000156, 4675000731, 4714000881, 4803000981, 4882000726, 4907000281, 5399000781, 5490000456, 5717000551, 5757000391, 5763000391, 5821000656, 6521000641, 6604000531, 6723000766, 6951000426, 7055000016, 7395000391, 7652000751, 7765000231, 8298000391, 8816000181, 8888000626, 9560000206, 9934000831, 10236000391, 10244000391, 10663000431, 10773000951, 10874000881, 11317000606, 11922000481, 12386000391, 12411000556, 13387000381, 13547000391, 13745000131, 13906000356, 14122000306, 14241000376, 14867000851, 15074000376, 15462000231, 15702000631, 15748000141, 15993000766, 15995000391, 15997000141, 15999000016, 16001000016, 16003000141, 16005000391, 16007000766, 16254000141, 17258000776, 17750000956, 17793000331, 17880000826, 18510000406, 18657000391, 19091000956, 20076000391, 20115000751, 20172000256, 20532000001, 20860000926, 21502000851, 22756000606, 22830000706, 23034000391, 23046000391, 23467000276, 24842000431, 25694000656, 26208000391, 26311000831, 26479000351, 27885000391, 28557000016, 29237000766, 29663000641, 31353000391, 31367000391, 31868000781, 33258000651, 33678000726, 35039000391, 35603000581, 35683000926, 35732000641, 36269000641, 36974000391, 37128000226, 38480000401, 39391000251, 39538000806, 39968000101, 40469000326, 40952000391, 40968000391, 41041000006, 42316000756, 42950000641, 43204000351, 43466000766, 44001000556, 44304000016, 45150000391, 47132000826, 47343000391, 47438000626, 48901000056, 49172000676, 50039000131, 51334000801, 51831000391, 51849000391, 52473000631, 54807000081, 56541000391, 57692000026, 58604000856, 58992000391, 61332000676, 62303000901, 62348000406, 62631000301, 63098000731, 63495000141, 63986000766, 63990000391, 63994000141, 63998000016, 64002000016, 64006000141, 64010000391, 64014000766, 64227000931, 64507000141, 66666000256, 67002000976, 68582000031, 68956000801, 69128000206, 69212000391, 69356000401, 70484000476, 71921000391, 73132000476, 73865000526, 75794000701, 77429000391, 77451000391, 78949000356, 79077000876, 79393000576, 82988000551, 83101000201, 83163000391, 83874000976, 84497000451, 85799000701, 86130000391, 87308000016, 88494000766, 89234000641, 90829000681, 91706000506, 92148000391, 92172000391, 96894000076, 98394000391, 99553000641, 100448000641, 101619000391, 103155000076, 108147000391, 108173000391, 108653000506, 109612000681, 111379000641, 112209000766, 113553000016, 114905000391, 115288000701, 116808000451, 117543000976, 118388000391, 118462000201, 118597000551, 122982000576, 123376000876, 123536000356, 125426000391, 125454000391, 127555000701, 130086000526, 131063000476, 132696000391, 134665000476, 136235000401, 136437000391, 136555000206.

Some larger examples :