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Duffinian n.  and  nonagonal n.

First numbers that belong to both sets:

9, 75, 111, 325, 559, 651, 1089, 1639, 2125, 3961, 4699, 6069, 7291, 8281, 10071, 11629, 12871, 18469, 21099, 23329, 25671, 30691, 32689, 38325, 39061, 41311, 45201, 48439, 50941, 51789, 55251, 61579, 70219, 82621, 85879, 86979, 91449, 96031, 99541, 110449, 114211, 119325, 120621, 129889, 142309, 146575, 159751, 164269, 171939, 182971, 197659, 202681, 223399, 232329, 239599, 245125, 246981, 262081, 267859, 285571, 291601, 310069, 316351, 342109, 389611, 396649, 408519, 418141, 425431, 447679, 455221, 467931, 478225, 486019, 509779, 542341, 550639, 553419, 564609, 573075, 575911, 584461, 610489, 619291, 655129, 658161, 670359, 682669, 695091, 729829, 755625, 758881, 768691, 785181, 798499, 808561, 811929, 825471, 839125, 849439, 880759, 891325, 923401, 934219, 967051, 978121, 1011709, 1026819, 1068949, 1072821, 1104049, 1163809, 1184079, 1200421, 1212751, 1250119, 1262701, 1313659, 1352539, 1370001, 1405261, 1458991, 1472581, 1513729, 1527571, 1532199, 1550781, 1626229, 1683991, 1698589, 1703469, 1723059, 1742761, 1757611, 1802539, 1817641, 1842951, 1878679, 1925119, 1987921, 2003779, 2051731, 2067841, 2094831, 2116549, 2132911, 2154825, 2198989, 2226819, 2249209, 2266075, 2271711, 2317051, 2334169, 2385901, 2403271, 2432361, 2455759, 2479269, 2544499, 2598499, 2616625, 2622681, 2671381, 2689759, 2745271, 2763901, 2864325, 2870661, 2915209, 2921601, 2972989, 2992375, 3050911, 3070549, 3077109, 3149731, 3209779, 3229921, 3317931, 3345249, 3372679, 3393325, 3455641, 3476539, 3539611, 3560761, 3624589, 3645991, 3653139, 3681801, 3732229, 3797569, 3826791, 3907729, 3915129, 3974581, 3996991, 4064599, 4087261, 4094829, 4178539, 4186191, 4216869, 4247659, 4270825, 4340701, 4364119, 4426875, 4434751, 4458421, 4498011, 4650049, 4690479, 4747375, 4821031, 4845709, 4920121, 4945051, 4986741, 5020219, 5045401, 5053809, 5146759, 5249125, 5326561, 5352499, 5361159, 5430691, 5456881, 5535829, 5562271, 5571099, 5668669, 5749129, 5857291, 5884489, 5929959, 5966461, 6076639, 6104341, 6215779, 6300019, 6337641, 6413221, 6441679, 6556141, 6604131, 6671611, 6788089, 6905575, 7024069, 7033989, 7073739, 7113601, 7143571, 7233859, 7304475, 7314591, 7385599, 7395771, 7436529, 7477399, 7508125, 7600681, 7631659, 7683429, 7724971, 7756201, 7881751, 8103889, 8135875, 8146551, 8232211, 8264449, 8361541, 8394031, 8491879, 8656219, 8755579, 8922439, 9023311, 9057061, 9158689, 9192691, 9249501, 9329329, 9432469, 9466975, 9570871, 9605629, 9710281, 9745291, 9850699, 9885961.